1
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Boffi NM, Vanden-Eijnden E. Deep learning probability flows and entropy production rates in active matter. Proc Natl Acad Sci U S A 2024; 121:e2318106121. [PMID: 38861599 PMCID: PMC11194503 DOI: 10.1073/pnas.2318106121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2023] [Accepted: 05/01/2024] [Indexed: 06/13/2024] Open
Abstract
Active matter systems, from self-propelled colloids to motile bacteria, are characterized by the conversion of free energy into useful work at the microscopic scale. They involve physics beyond the reach of equilibrium statistical mechanics, and a persistent challenge has been to understand the nature of their nonequilibrium states. The entropy production rate and the probability current provide quantitative ways to do so by measuring the breakdown of time-reversal symmetry. Yet, their efficient computation has remained elusive, as they depend on the system's unknown and high-dimensional probability density. Here, building upon recent advances in generative modeling, we develop a deep learning framework to estimate the score of this density. We show that the score, together with the microscopic equations of motion, gives access to the entropy production rate, the probability current, and their decomposition into local contributions from individual particles. To represent the score, we introduce a spatially local transformer network architecture that learns high-order interactions between particles while respecting their underlying permutation symmetry. We demonstrate the broad utility and scalability of the method by applying it to several high-dimensional systems of active particles undergoing motility-induced phase separation (MIPS). We show that a single network trained on a system of 4,096 particles at one packing fraction can generalize to other regions of the phase diagram, including to systems with as many as 32,768 particles. We use this observation to quantify the spatial structure of the departure from equilibrium in MIPS as a function of the number of particles and the packing fraction.
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Affiliation(s)
- Nicholas M. Boffi
- Courant Institute of Mathematical Sciences, New York University, New York, NY10012
| | - Eric Vanden-Eijnden
- Courant Institute of Mathematical Sciences, New York University, New York, NY10012
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2
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Keta YE, Klamser JU, Jack RL, Berthier L. Emerging Mesoscale Flows and Chaotic Advection in Dense Active Matter. PHYSICAL REVIEW LETTERS 2024; 132:218301. [PMID: 38856251 DOI: 10.1103/physrevlett.132.218301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2023] [Revised: 11/23/2023] [Accepted: 04/17/2024] [Indexed: 06/11/2024]
Abstract
We study two models of overdamped self-propelled disks in two dimensions, with and without aligning interactions. Both models support active mesoscale flows, leading to chaotic advection and transport over large length scales in their homogeneous dense fluid states, away from dynamical arrest. They form streams and vortices reminiscent of multiscale flow patterns in turbulence. We show that the characteristics of these flows do not depend on the specific details of the active fluids, and result from the competition between crowding effects and persistent propulsions. This observation suggests that dense active suspensions of self-propelled particles present a type of "active turbulence" distinct from collective flows reported in other types of active systems.
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Affiliation(s)
- Yann-Edwin Keta
- Laboratoire Charles Coulomb (L2C), Université de Montpellier and CNRS (UMR 5221), 34095 Montpellier, France
| | - Juliane U Klamser
- Laboratoire Charles Coulomb (L2C), Université de Montpellier and CNRS (UMR 5221), 34095 Montpellier, France
| | - Robert L Jack
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Ludovic Berthier
- Laboratoire Charles Coulomb (L2C), Université de Montpellier and CNRS (UMR 5221), 34095 Montpellier, France
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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3
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Semeraro M, Suma A, Negro G. Fluctuation Theorems for Heat Exchanges between Passive and Active Baths. ENTROPY (BASEL, SWITZERLAND) 2024; 26:439. [PMID: 38920448 PMCID: PMC11203073 DOI: 10.3390/e26060439] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2024] [Revised: 05/17/2024] [Accepted: 05/19/2024] [Indexed: 06/27/2024]
Abstract
In addition to providing general constraints on probability distributions, fluctuation theorems allow us to infer essential information on the role played by temperature in heat exchange phenomena. In this numerical study, we measure the temperature of an out-of-equilibrium active bath using a fluctuation theorem that relates the fluctuations in the heat exchanged between two baths to their temperatures. Our setup consists of a single particle moving between two wells of a quartic potential accommodating two different baths. The heat exchanged between the two baths is monitored according to two definitions: as the kinetic energy carried by the particle whenever it jumps from one well to the other and as the work performed by the particle on one of the two baths when immersed in it. First, we consider two equilibrium baths at two different temperatures and verify that a fluctuation theorem featuring the baths temperatures holds for both heat definitions. Then, we introduce an additional Gaussian coloured noise in one of the baths, so as to make it effectively an active (out-of-equilibrium) bath. We find that a fluctuation theorem is still satisfied with both heat definitions. Interestingly, in this case the temperature obtained through the fluctuation theorem for the active bath corresponds to the kinetic temperature when considering the first heat definition, while it is larger with the second one. We interpret these results by looking at the particle jump phenomenology.
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Affiliation(s)
- Massimiliano Semeraro
- Dipartimento Interateneo di Fisica, Università degli Studi di Bari and INFN, Sezione di Bari, Via Amendola 173, 70126 Bari, Italy; (A.S.); (G.N.)
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4
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Adersh F, Muhsin M, Sahoo M. Inertial active harmonic particle with memory induced spreading by viscoelastic suspension. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2024; 47:33. [PMID: 38753070 DOI: 10.1140/epje/s10189-024-00424-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2024] [Accepted: 04/15/2024] [Indexed: 06/11/2024]
Abstract
We investigate the self-propulsion of an inertial active particle confined in a two-dimensional harmonic trap. The particle is suspended in a non-Newtonian or viscoelastic suspension with a friction kernel that decays exponentially with a time constant characterizing the memory timescale or transient elasticity of the medium. By solving the associated non-Markovian dynamics, we identify two regimes in parameter space distinguishing the oscillatory and non-oscillatory behavior of the particle motion. By simulating the particle trajectories and exactly calculating the steady-state probability distribution functions and mean square displacement; interestingly, we observe that with an increase in the memory time scale, the effective temperature of the environment increases. As a consequence, the particle becomes energetic and spread away from the center, covering larger space inside the confinement. On the other hand, with an increase in the duration of the activity, the particle becomes trapped by the harmonic confinement.
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Affiliation(s)
- F Adersh
- Department of Physics, University of Kerala, Kariavattom, Thiruvananthapuram, 695581, India
| | - M Muhsin
- Department of Physics, University of Kerala, Kariavattom, Thiruvananthapuram, 695581, India
| | - M Sahoo
- Department of Physics, University of Kerala, Kariavattom, Thiruvananthapuram, 695581, India.
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5
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Yadav RS, Sharma S, Metzler R, Chakrabarti R. A passive star polymer in a dense active bath: insights from computer simulations. SOFT MATTER 2024; 20:3910-3922. [PMID: 38700098 DOI: 10.1039/d4sm00144c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2024]
Abstract
Using computer simulations in two dimensions (2D), we explore the structure and dynamics of a star polymer with three arms made of passive monomers immersed in a bath of active Brownian particles (ABPs). We analyze the conformational and dynamical changes of the polymer as a function of activity and packing fraction. We also study the process of motility induced phase separation (MIPS) in the presence of a star polymer, which acts as a mobile nucleation center. The presence of the polymer increases the growth rate of the clusters in comparison to a bath without the polymer. In particular, for low packing fraction, both nucleation and cluster growth are affected by the inclusion of the star polymer. Clusters grow in the vicinity of the star polymer, resulting in the star polymer experiencing a caged motion similar to a tagged ABP in the dense phase. Due to the topological constraints of the star polymers and clustering nearby, the conformational changes of the star polymer lead to interesting observations. Inter alia, we observe the shrinking of the arm with increasing activity along with a short-lived hairpin structure of one arm formed. We also see the transient pairing of two arms of the star polymer, while the third is largely separated at high activity. We hope our findings will help in understanding the behavior of active-passive mixtures, including biopolymers of complex topology in dense active suspensions.
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Affiliation(s)
- Ramanand Singh Yadav
- Department of Chemistry, Indian Institute of Technology Bombay, Mumbai 400076, India.
| | - Sanaa Sharma
- Department of Chemistry, Indian Institute of Technology Bombay, Mumbai 400076, India.
| | - Ralf Metzler
- Institute of Physics and Astronomy, University of Potsdam, Germany.
- Asia Pacific Center for Theoretical Physics, Pohang 37673, Republic of Korea
| | - Rajarshi Chakrabarti
- Department of Chemistry, Indian Institute of Technology Bombay, Mumbai 400076, India.
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6
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Polley K, Wilson KR, Limmer DT. On the Statistical Mechanics of Mass Accommodation at Liquid-Vapor Interfaces. J Phys Chem B 2024; 128:4148-4157. [PMID: 38652843 DOI: 10.1021/acs.jpcb.4c00899] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/25/2024]
Abstract
We propose a framework for describing the dynamics associated with the adsorption of small molecules to liquid-vapor interfaces using an intermediate resolution between traditional continuum theories that are bereft of molecular detail and molecular dynamics simulations that are replete with them. In particular, we develop an effective single particle equation of motion capable of describing the physical processes that determine thermal and mass accommodation probabilities. The effective equation is parametrized with quantities that vary through space away from the liquid-vapor interface. Of particular importance in describing the early time dynamics is the spatially dependent friction, for which we propose a numerical scheme to evaluate from molecular simulation. Taken together with potentials of mean force computable with importance sampling methods, we illustrate how to compute the mass accommodation coefficient and residence time distribution. Throughout, we highlight the case of ozone adsorption in aqueous solutions and its dependence on electrolyte composition.
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Affiliation(s)
- Kritanjan Polley
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Kevin R Wilson
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - David T Limmer
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- Kavli Energy NanoScience Institute, Berkeley, California 94720, United States
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7
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Silvano N, Barci DG. Emergent gauge symmetry in active Brownian matter. Phys Rev E 2024; 109:044605. [PMID: 38755850 DOI: 10.1103/physreve.109.044605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2023] [Accepted: 04/04/2024] [Indexed: 05/18/2024]
Abstract
We investigate a two-dimensional system of interacting active Brownian particles. Using the Martin-Siggia-Rose-Janssen-de Dominicis formalism, we built up the generating functional for correlation functions. We study in detail the hydrodynamic regime with a constant density stationary state. Our findings reveal that, within a small density fluctuations regime, an emergent U(1) gauge symmetry arises, originated from the conservation of fluid vorticity. Consequently, the interaction between the orientational order parameter and density fluctuations can be cast into a gauge theory, where the concept of "electric charge density" aligns with the local vorticity of the original fluid. We study in detail the case of a microscopic local two-body interaction. We show that, upon integrating out the gauge fields, the stationary states of the rotational degrees of freedom satisfy a nonlocal Frank free energy for a nematic fluid. We give explicit expressions for the splay and bend elastic constants as a function of the Péclet number (Pe) and the diffusion interaction constant (k_{d}).
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Affiliation(s)
- Nathan Silvano
- Center for Advanced Systems Understanding, Untermarkt 20, 02826 Görlitz, Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstraße 400, 01328 Dresden, Germany
- Departamento de Física Teórica, 20270-004 Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, 20550-013, Rio de Janeiro, RJ, Brazil
| | - Daniel G Barci
- Departamento de Física Teórica, 20270-004 Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, 20550-013, Rio de Janeiro, RJ, Brazil
- Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589, 4 Place Jussieu, 75252 Paris Cedex 05, France
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8
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Kwon T, Kwon S, Sung BJ. The effects of asymmetry in active noises on the efficiency of single colloidal Stirling engines with active noises. SOFT MATTER 2024; 20:2600-2609. [PMID: 38426540 DOI: 10.1039/d3sm01386c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/02/2024]
Abstract
Molecular machines, which operate in highly fluctuating environments far from equilibrium, may benefit from their non-equilibrium environments. It is, however, a topic of controversy how the efficiency of the microscopic engines can be enhanced. Recent experiments showed that microscopic Stirling engines in bacterial reservoirs could show high performance beyond the equilibrium thermodynamics. In this work, we perform overdamped Langevin dynamics simulations for microscopic Stirling heat engines in bacterial reservoirs and show that the temperature dependence of the magnitude of active noises should be responsible for such high efficiency. Only when we introduce temperature-dependent active noises, the efficiency of the microscopic Stirling engines is enhanced significantly as in experiments.
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Affiliation(s)
- Taejin Kwon
- Department of Chemistry and Cosmetics, Jeju National University, Jeju 63243, Republic of Korea
| | - Seulki Kwon
- The Center for the Development of Therapeutics, Broad Institute of MIT and Harvard, Cambridge, MA 02142, USA
| | - Bong June Sung
- Department of Chemistry, Sogang University, Seoul 04107, Republic of Korea.
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9
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Spera G, Duclut C, Durand M, Tailleur J. Nematic Torques in Scalar Active Matter: When Fluctuations Favor Polar Order and Persistence. PHYSICAL REVIEW LETTERS 2024; 132:078301. [PMID: 38427854 DOI: 10.1103/physrevlett.132.078301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2023] [Revised: 07/12/2023] [Accepted: 01/08/2024] [Indexed: 03/03/2024]
Abstract
We study the impact of nematic alignment on scalar active matter in the disordered phase. We show that nematic torques control the emergent physics of particles interacting via pairwise forces and can either induce or prevent phase separation. The underlying mechanism is a fluctuation-induced renormalization of the mass of the polar field that generically arises from nematic torques. The correlations between the fluctuations of the polar and nematic fields indeed conspire to increase the particle persistence length, contrary to what phenomenological computations predict. This effect is generic and our theory also quantitatively accounts for how nematic torques enhance particle accumulation along confining boundaries and opposes demixing in mixtures of active and passive particles.
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Affiliation(s)
- Gianmarco Spera
- Université Paris Cité, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France
| | - Charlie Duclut
- Université Paris Cité, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France
- Laboratoire Physique des Cellules et Cancer (PCC), CNRS UMR 168, Institut Curie, Université PSL, Sorbonne Université, 75005 Paris, France
| | - Marc Durand
- Université Paris Cité, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France
| | - Julien Tailleur
- Université Paris Cité, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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10
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Du M, Behera AK, Vaikuntanathan S. Active oscillatory associative memory. J Chem Phys 2024; 160:055103. [PMID: 38341712 DOI: 10.1063/5.0171983] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2023] [Accepted: 01/07/2024] [Indexed: 02/13/2024] Open
Abstract
Traditionally, physical models of associative memory assume conditions of equilibrium. Here, we consider a prototypical oscillator model of associative memory and study how active noise sources that drive the system out of equilibrium, as well as nonlinearities in the interactions between the oscillators, affect the associative memory properties of the system. Our simulations show that pattern retrieval under active noise is more robust to the number of learned patterns and noise intensity than under passive noise. To understand this phenomenon, we analytically derive an effective energy correction due to the temporal correlations of active noise in the limit of short correlation decay time. We find that active noise deepens the energy wells corresponding to the patterns by strengthening the oscillator couplings, where the more nonlinear interactions are preferentially enhanced. Using replica theory, we demonstrate qualitative agreement between this effective picture and the retrieval simulations. Our work suggests that the nonlinearity in the oscillator couplings can improve memory under nonequilibrium conditions.
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Affiliation(s)
- Matthew Du
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, USA
- The James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
| | - Agnish Kumar Behera
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, USA
| | - Suriyanarayanan Vaikuntanathan
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, USA
- The James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
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11
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Valido AA, Coccolo M, Sanjuán MAF. Time-delayed Duffing oscillator in an active bath. Phys Rev E 2023; 108:064205. [PMID: 38243436 DOI: 10.1103/physreve.108.064205] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2023] [Accepted: 11/17/2023] [Indexed: 01/21/2024]
Abstract
During recent decades active particles have attracted an incipient attention as they have been observed in a broad class of scenarios, ranging from bacterial suspension in living systems to artificial swimmers in nonequilibirum systems. The main feature of these particles is that they are able to gain kinetic energy from the environment, which is widely modeled by a stochastic process due to both (Gaussian) white and Ornstein-Uhlenbeck noises. In the present work, we study the nonlinear dynamics of the forced, time-delayed Duffing oscillator subject to these noises, paying special attention to their impact upon the maximum oscillations amplitude and characteristic frequency of the steady state for different values of the time delay and the driving force. Overall, our results indicate that the role of the time delay is substantially modified with respect to the situation without noise. For instance, we show that the oscillations amplitude grows with increasing noise strength when the time delay acts as a damping term in absence of noise, whereas the trajectories eventually become aperiodic when the oscillations are sustained by the time delay. In short, the interplay among the noises, forcing, and time delay gives rise to a rich dynamics: a regular and periodic motion is destroyed or restored owing to the competition between the noise and the driving force depending on time delay values, whereas an erratic motion insensitive to the driving force emerges when the time delay makes the motion aperiodic. Interestingly, we also show that, for a sufficient noise strength and forcing amplitude, an approximately periodic interwell motion is promoted by means of stochastic resonance.
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Affiliation(s)
- Antonio A Valido
- Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain
| | - Mattia Coccolo
- Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain
| | - Miguel A F Sanjuán
- Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain
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12
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Dinelli A, O'Byrne J, Curatolo A, Zhao Y, Sollich P, Tailleur J. Non-reciprocity across scales in active mixtures. Nat Commun 2023; 14:7035. [PMID: 37923724 PMCID: PMC10624904 DOI: 10.1038/s41467-023-42713-5] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2023] [Accepted: 10/19/2023] [Indexed: 11/06/2023] Open
Abstract
In active matter, particles typically experience mediated interactions, which are not constrained by Newton's third law and are therefore generically non-reciprocal. Non-reciprocity leads to a rich set of emerging behaviors that are hard to account for starting from the microscopic scale, due to the absence of a generic theoretical framework out of equilibrium. Here we consider bacterial mixtures that interact via mediated, non-reciprocal interactions (NRI) like quorum-sensing and chemotaxis. By explicitly relating microscopic and macroscopic dynamics, we show that, under conditions that we derive explicitly, non-reciprocity may fade upon coarse-graining, leading to large-scale equilibrium descriptions. In turn, this allows us to account quantitatively, and without fitting parameters, for the rich behaviors observed in microscopic simulations including phase separation, demixing, and multi-phase coexistence. We also derive the condition under which non-reciprocity survives coarse-graining, leading to a wealth of dynamical patterns. Again, our analytical approach allows us to predict the phase diagram of the system starting from its microscopic description. All in all, our work demonstrates that the fate of non-reciprocity across scales is a subtle and important question.
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Affiliation(s)
- Alberto Dinelli
- Université Paris Cité, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205, Paris, France
| | - Jérémy O'Byrne
- Université Paris Cité, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205, Paris, France
- Department of Applied Maths and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Rd, Cambridge, CB3 0WA, UK
| | - Agnese Curatolo
- John A. Paulson School of Engineering and Applied Sciences and Kavli Institute for Bionano Science and Technology, Harvard University, Cambridge, MA, 02138, USA
| | - Yongfeng Zhao
- Center for Soft Condensed Matter Physics and Interdisciplinary Research & School of Physical Science and Technology, Soochow University, 215006, Suzhou, China
| | - Peter Sollich
- Institute for Theoretical Physics, Georg-August-Universität Göttingen, 37 077, Göttingen, Germany
- Department of Mathematics, King's College London, London, WC2R 2LS, UK
| | - Julien Tailleur
- Université Paris Cité, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205, Paris, France.
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA.
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13
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Cocconi L, Knight J, Roberts C. Optimal Power Extraction from Active Particles with Hidden States. PHYSICAL REVIEW LETTERS 2023; 131:188301. [PMID: 37977620 DOI: 10.1103/physrevlett.131.188301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2023] [Revised: 05/23/2023] [Accepted: 10/12/2023] [Indexed: 11/19/2023]
Abstract
We identify generic protocols achieving optimal power extraction from a single active particle subject to continuous feedback control under the assumption that its spatial trajectory, but not its instantaneous self-propulsion force, is accessible to direct observation. Our Bayesian approach draws on the Onsager-Machlup path integral formalism and is exemplified in the cases of free run-and-tumble and active Ornstein-Uhlenbeck dynamics in one dimension. Such optimal protocols extract positive work even in models characterized by time-symmetric positional trajectories and thus vanishing informational entropy production rates. We argue that the theoretical bounds derived in this work are those against which the performance of realistic active matter engines should be compared.
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Affiliation(s)
- Luca Cocconi
- The Francis Crick Institute, London NW1 1AT, United Kingdom
- Department of Mathematics, Imperial College London, South Kensington, London SW7 2BZ, United Kingdom
| | - Jacob Knight
- Department of Mathematics, Imperial College London, South Kensington, London SW7 2BZ, United Kingdom
| | - Connor Roberts
- Department of Mathematics, Imperial College London, South Kensington, London SW7 2BZ, United Kingdom
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14
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Semeraro M, Gonnella G, Suma A, Zamparo M. Work Fluctuations for a Harmonically Confined Active Ornstein-Uhlenbeck Particle. PHYSICAL REVIEW LETTERS 2023; 131:158302. [PMID: 37897759 DOI: 10.1103/physrevlett.131.158302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2023] [Accepted: 09/13/2023] [Indexed: 10/30/2023]
Abstract
We study the active work fluctuations of an active Ornstein-Uhlenbeck particle in the presence of a confining harmonic potential. We tackle the problem analytically both for stationary and generic uncorrelated initial states. Our results show that harmonic confinement can induce singularities in the active work rate function, with linear stretches at large positive and negative active work, at sufficiently large active and harmonic force constants. These singularities originate from big jumps in the displacement and in the active force, occurring at the initial or ending points of trajectories and marking the relevance of boundary terms in this problem.
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Affiliation(s)
- Massimiliano Semeraro
- Dipartimento Interateneo di Fisica, Università degli Studi di Bari and INFN, Sezione di Bari, via Amendola 173, Bari I-70126, Italy
| | - Giuseppe Gonnella
- Dipartimento Interateneo di Fisica, Università degli Studi di Bari and INFN, Sezione di Bari, via Amendola 173, Bari I-70126, Italy
| | - Antonio Suma
- Dipartimento Interateneo di Fisica, Università degli Studi di Bari and INFN, Sezione di Bari, via Amendola 173, Bari I-70126, Italy
| | - Marco Zamparo
- Dipartimento Interateneo di Fisica, Università degli Studi di Bari and INFN, Sezione di Bari, via Amendola 173, Bari I-70126, Italy
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15
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Caprini L, Marini Bettolo Marconi U, Löwen H. Entropy production and collective excitations of crystals out of equilibrium: The concept of entropons. Phys Rev E 2023; 108:044603. [PMID: 37978682 DOI: 10.1103/physreve.108.044603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2023] [Accepted: 09/21/2023] [Indexed: 11/19/2023]
Abstract
We study the collective vibrational excitations of crystals under out-of-equilibrium steady conditions that give rise to entropy production. Their excitation spectrum comprises equilibriumlike phonons of thermal origin and additional collective excitations called entropons because each of them represents a mode of spectral entropy production. Entropons coexist with phonons and dominate them when the system is far from equilibrium while they are negligible in near-equilibrium regimes. The concept of entropons has been recently introduced and verified in a special case of crystals formed by self-propelled particles. Here we show that entropons exist in a broader class of active crystals that are intrinsically out of equilibrium and characterized by the lack of detailed balance. After a general derivation, several explicit examples are discussed, including crystals consisting of particles with alignment interactions and frictional contact forces.
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Affiliation(s)
- L Caprini
- Heinrich-Heine-Universität Düsseldorf, Institut für Theoretische Physik II: Weiche Materie, Universitätsstrasse, 40225 Düsseldorf, Germany
| | - U Marini Bettolo Marconi
- Physics Department, Scuola di Scienze e Tecnologie, Università di Camerino - via Madonna delle Carceri, 62032 Camerino, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, Via A. Pascoli, 06123 Perugia, Italy
| | - H Löwen
- Heinrich-Heine-Universität Düsseldorf, Institut für Theoretische Physik II: Weiche Materie, Universitätsstrasse, 40225 Düsseldorf, Germany
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16
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Nakul U, Roy S, Nalupurackal G, Chakraborty S, Siwach P, Goswami J, Edwina P, Bajpai SK, Singh R, Roy B. Studying fluctuating trajectories of optically confined passive tracers inside cells provides familiar active forces. BIOMEDICAL OPTICS EXPRESS 2023; 14:5440. [PMID: 37810271 PMCID: PMC7615170 DOI: 10.1364/boe.499990] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2023] [Revised: 08/14/2023] [Accepted: 09/05/2023] [Indexed: 10/10/2023]
Abstract
In recent years, there has been a growing interest in studying the trajectories of microparticles inside living cells. Among other things, such studies are useful in understanding the spatio-temporal properties of a cell. In this work, we study the stochastic trajectories of a passive microparticle inside a cell using experiments and theory. Our theory is based on modeling the microparticle inside a cell as an active particle in a viscoelastic medium. The activity is included in our model from an additional stochastic term with non-zero persistence in the Langevin equation describing the dynamics of the microparticle. Using this model, we are able to predict the power spectral density (PSD) measured in the experiment and compute active forces. This caters to the situation where a tracer particle is optically confined and then yields a PSD for positional fluctuations. The low frequency part of the PSD yields information about the active forces that the particle feels. The fit to the model extracts such active force. Thus, we can conclude that trapping the particle does not affect the values of the forces extracted from the active fits if accounted for appropriately by proper theoretical models. In addition, the fit also provides system properties and optical tweezers trap stiffness.
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Affiliation(s)
- Urvashi Nakul
- Department of Physics, Quantum Centre of Excellence for Diamond and Emergent Materials (QuCenDiEM), IIT Madras, Chennai 600036, India
| | - Srestha Roy
- Department of Physics, Quantum Centre of Excellence for Diamond and Emergent Materials (QuCenDiEM), IIT Madras, Chennai 600036, India
| | - Gokul Nalupurackal
- Department of Physics, Quantum Centre of Excellence for Diamond and Emergent Materials (QuCenDiEM), IIT Madras, Chennai 600036, India
| | - Snigdhadev Chakraborty
- Department of Physics, Quantum Centre of Excellence for Diamond and Emergent Materials (QuCenDiEM), IIT Madras, Chennai 600036, India
| | - Priyanka Siwach
- Department of Physics, Quantum Centre of Excellence for Diamond and Emergent Materials (QuCenDiEM), IIT Madras, Chennai 600036, India
| | - Jayesh Goswami
- Department of Physics, Quantum Centre of Excellence for Diamond and Emergent Materials (QuCenDiEM), IIT Madras, Chennai 600036, India
| | - Privita Edwina
- Department of Physics, Quantum Centre of Excellence for Diamond and Emergent Materials (QuCenDiEM), IIT Madras, Chennai 600036, India
- Department of Applied Mechanics, IIT Madras, Chennai 600036, India
| | | | - Rajesh Singh
- Department of Physics, IIT Madras, Chennai 600036, India
| | - Basudev Roy
- Department of Physics, Quantum Centre of Excellence for Diamond and Emergent Materials (QuCenDiEM), IIT Madras, Chennai 600036, India
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17
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Kasuga K, Yoshimori A. Nonintegral form of the reciprocal relation associated with violation of the fluctuation response relation. Phys Rev E 2023; 108:034109. [PMID: 37849163 DOI: 10.1103/physreve.108.034109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2022] [Accepted: 08/15/2023] [Indexed: 10/19/2023]
Abstract
We extend Onsager's reciprocal relation to systems in a nonequilibrium steady state. While Onsager's reciprocal relation concerns the kinetic (Onsager) coefficient, the extended reciprocal relation concerns violation of the fluctuation response relation (FRR) for mechanical and thermal perturbations. This extended relation holds at each frequency when the extent of the FRR violation is expressed in a frequency domain. This nonintegral form distinguishes the extended relation from previous relations expressed by integration over a frequency. To obtain this relation, we consider one-particle one-dimensional systems described by an overdamped Langevin equation with a force driving the system away from equilibrium. We assume a special property of the potential in the system. From this Langevin equation, we obtain the Fokker-Planck (FP) equation describing the time evolution of the distribution function of the particle. Using the FP equation, we calculate the responses of the particle velocity and heat current by applying time-dependent perturbations of the driving force and temperature. We express the extent of the FRR violation in terms of these responses with time correlation functions and expand them in powers of the FP operator. This reciprocal relation is valid far from equilibrium. One can also confirm this reciprocal relation through experiments with systems such as colloidal suspensions because the FRR violation can be experimentally observed.
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Affiliation(s)
- Kotaro Kasuga
- Department of Physics, Niigata University, Niigata 950-2181, Japan
| | - Akira Yoshimori
- Department of Physics, Niigata University, Niigata 950-2181, Japan
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18
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Caprini L, Löwen H, Marini Bettolo Marconi U. Chiral active matter in external potentials. SOFT MATTER 2023; 19:6234-6246. [PMID: 37555622 DOI: 10.1039/d3sm00793f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/10/2023]
Abstract
We investigate the interplay between chirality and confinement induced by the presence of an external potential. For potentials having radial symmetry, the circular character of the trajectories induced by the chiral motion reduces the spatial fluctuations of the particle, thus providing an extra effective confining mechanism, that can be interpreted as a lowering of the effective temperature. In the case of non-radial potentials, for instance, with an elliptic shape, chirality displays a richer scenario. Indeed, the chirality can break the parity symmetry of the potential that is always fulfilled in the non-chiral system. The probability distribution displays a strong non-Maxwell-Boltzmann shape that emerges in cross-correlations between the two Cartesian components of the position, that vanishes in the absence of chirality or when radial symmetry of the potential is restored. These results are obtained by considering two popular models in active matter, i.e. chiral Active Brownian particles and chiral active Ornstein-Uhlenbeck particles.
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Affiliation(s)
- Lorenzo Caprini
- Heinrich-Heine-Universität Düsseldorf, Institut für Theoretische Physik II - Weiche Materie, D-40225 Düsseldorf, Germany.
| | - Hartmut Löwen
- Heinrich-Heine-Universität Düsseldorf, Institut für Theoretische Physik II - Weiche Materie, D-40225 Düsseldorf, Germany.
| | - Umberto Marini Bettolo Marconi
- Scuola di Scienze e Tecnologie, Università di Camerino - via Madonna delle Carceri, 62032, Camerino, Italy
- INFN Sezione di Perugia, I-06123 Perugia, Italy.
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19
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Gupta D, Klapp SHL, Sivak DA. Efficient control protocols for an active Ornstein-Uhlenbeck particle. Phys Rev E 2023; 108:024117. [PMID: 37723713 DOI: 10.1103/physreve.108.024117] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2023] [Accepted: 07/11/2023] [Indexed: 09/20/2023]
Abstract
Designing a protocol to efficiently drive a stochastic system is an active field of research. Here we extend such control theory to an active Ornstein-Uhlenbeck particle (AOUP) in a bistable potential, driven by a harmonic trap. We find that protocols designed to minimize the excess work (up to linear response) perform better than naive protocols with constant velocity for a wide range of protocol durations.
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Affiliation(s)
- Deepak Gupta
- Nordita, Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden
- Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
- Institut für Theoretische Physik, Hardenbergstr. 36, Technische Universität Berlin, D-10623 Berlin, Germany
| | - Sabine H L Klapp
- Institut für Theoretische Physik, Hardenbergstr. 36, Technische Universität Berlin, D-10623 Berlin, Germany
| | - David A Sivak
- Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
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20
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Caprini L, Marini Bettolo Marconi U, Puglisi A, Löwen H. Entropons as collective excitations in active solids. J Chem Phys 2023; 159:041102. [PMID: 37486049 DOI: 10.1063/5.0156312] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2023] [Accepted: 07/05/2023] [Indexed: 07/25/2023] Open
Abstract
The vibrational dynamics of solids is described by phonons constituting basic collective excitations in equilibrium crystals. Here, we consider a non-equilibrium active solid, formed by self-propelled particles, which bring the system into a non-equilibrium steady-state. We identify novel vibrational collective excitations of non-equilibrium (active) origin, which coexist with phonons and dominate over them when the system is far from equilibrium. These vibrational excitations are interpreted in the framework of non-equilibrium physics, in particular, stochastic thermodynamics. We call them "entropons" because they are the modes of spectral entropy production (at a given frequency and wave vector). The existence of entropons could be verified in future experiments on dense self-propelled colloidal Janus particles and granular active matter, as well as in living systems, such as dense cell monolayers.
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Affiliation(s)
- Lorenzo Caprini
- Heinrich-Heine-Universität Düsseldorf, Institut für Theoretische Physik II-Weiche Materie, D-40225 Düsseldorf, Germany
| | - Umberto Marini Bettolo Marconi
- Scuola di Scienze e Tecnologie, Università di Camerino, via Madonna delle Carceri, 62032 Camerino, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, Via A. Pascoli, I-06123 Perugia, Italy
| | - Andrea Puglisi
- Istituto dei Sistemi Complessi-CNR and Università di Roma Sapienza, P.le Aldo Moro 2, 00185 Rome, Italy
- INFN, University of Rome Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - Hartmut Löwen
- Heinrich-Heine-Universität Düsseldorf, Institut für Theoretische Physik II-Weiche Materie, D-40225 Düsseldorf, Germany
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21
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Roberts C, Zhen Z. Run-and-tumble motion in a linear ratchet potential: Analytic solution, power extraction, and first-passage properties. Phys Rev E 2023; 108:014139. [PMID: 37583167 DOI: 10.1103/physreve.108.014139] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2023] [Accepted: 06/29/2023] [Indexed: 08/17/2023]
Abstract
We explore the properties of run-and-tumble particles moving in a piecewise-linear "ratchet" potential by deriving analytic results for the system's steady-state probability density, current, entropy production rate, extractable power, and thermodynamic efficiency. The ratchet's broken spatial symmetry rectifies the particles' self-propelled motion, resulting in a positive current that peaks at finite values of the diffusion strength, ratchet height, and particle self-propulsion speed. Similar nonmonotonic behavior is also observed for the extractable power and efficiency. We find the optimal apex position for generating maximum current varies with diffusion and that entropy production can have nonmonotonic dependence on diffusion. In particular, for vanishing diffusion, entropy production remains finite when particle self-propulsion is weaker than the ratchet force. Furthermore, power extraction with near-perfect efficiency is achievable in certain parameter regimes due to the simplifications afforded by modeling "dry" active particles. In the final part, we derive mean first-passage times and splitting probabilities for different boundary and initial conditions. This work connects the study of work extraction from active matter with exactly solvable active particle models and will therefore facilitate the design of active engines through these analytic results.
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Affiliation(s)
- Connor Roberts
- Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom and Centre for Complexity Science, Imperial College London SW7 2AZ, United Kingdom
| | - Zigan Zhen
- Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom and Centre for Complexity Science, Imperial College London SW7 2AZ, United Kingdom
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22
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Szamel G. Single active particle in a harmonic potential: Question about the existence of the Jarzynski relation. Phys Rev E 2023; 107:054602. [PMID: 37329101 DOI: 10.1103/physreve.107.054602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2022] [Accepted: 04/21/2023] [Indexed: 06/18/2023]
Abstract
The interest in active matter stimulates the need to generalize thermodynamic description and relations to active matter systems, which are intrinsically out of equilibrium. One important example is the Jarzynski relation, which links the exponential average of work done in an arbitrary process connecting two equilibrium states with the difference of the free energies of these states. Using a simple model system, a single thermal active Ornstein-Uhlenbeck particle in a harmonic potential, we show that if the standard stochastic thermodynamics definition of work is used, the Jarzynski relation is not generally valid for processes connecting stationary states of active matter systems.
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Affiliation(s)
- Grzegorz Szamel
- Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, USA
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23
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Muhsin M, Sahoo M. Inertial active ratchet: Simulation versus theory. Phys Rev E 2023; 107:054601. [PMID: 37329079 DOI: 10.1103/physreve.107.054601] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2022] [Accepted: 04/21/2023] [Indexed: 06/18/2023]
Abstract
We present the inertial active dynamics of an Ornstein-Uhlenbeck particle in a piecewise sawtooth ratchet potential. Using the Langevin simulation and matrix continued fraction method (MCFM), the particle transport, steady-state diffusion, and coherence in transport are investigated in different parameter regimes of the model. Spatial asymmetry is found to be a key criterion for the possibility of directed transport in the ratchet. The MCFM results for net particle current of overdamped dynamics of the particle agree well with the simulation results. The simulated particle trajectories for the inertial dynamics and the corresponding position and velocity distribution functions reveal that the system passes through an activity-induced transition in the transport from the running phase to the locked phase of the dynamics. This is further corroborated by the mean square displacement (MSD) calculations, where the MSD gets suppressed with increase in the persistent duration of activity or self-propulsion in the medium and finally approaches zero for a very large value of self propulsion time. The nonmonotonic behavior of the particle current and Péclet number with self-propulsion time confirms that the particle transport and its coherence can be enhanced or reduced by fine tuning the persistent duration of activity. Moreover, for intermediate ranges of self-propulsion time as well as mass of the particle, even though the particle current shows a pronounced unusual maximum with mass, there is no enhancement in the Péclet number, instead the Péclet number decreases with mass, confirming the degradation of coherence in transport.
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Affiliation(s)
- M Muhsin
- Department of Physics, University of Kerala, Kariavattom, Thiruvananthapuram-695581, India
| | - M Sahoo
- Department of Physics, University of Kerala, Kariavattom, Thiruvananthapuram-695581, India
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24
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O'Byrne J. Nonequilibrium currents in stochastic field theories: A geometric insight. Phys Rev E 2023; 107:054105. [PMID: 37329107 DOI: 10.1103/physreve.107.054105] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2023] [Accepted: 04/03/2023] [Indexed: 06/18/2023]
Abstract
We introduce a formalism to study nonequilibrium steady-state probability currents in stochastic field theories. We show that generalizing the exterior derivative to functional spaces allows identification of the subspaces in which the system undergoes local rotations. In turn, this allows prediction of the counterparts in the real, physical space of these abstract probability currents. The results are presented for the case of the Active Model B undergoing motility-induced phase separation, which is known to be out of equilibrium but whose steady-state currents have not yet been observed, as well as for the Kardar-Parisi-Zhang equation. We locate and measure these currents and show that they manifest in real space as propagating modes localized in regions with nonvanishing gradients of the fields.
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Affiliation(s)
- J O'Byrne
- Université Paris-Cité, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France and DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
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25
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Sprenger AR, Caprini L, Löwen H, Wittmann R. Dynamics of active particles with translational and rotational inertia. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 35:305101. [PMID: 37059111 DOI: 10.1088/1361-648x/accd36] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2023] [Accepted: 04/14/2023] [Indexed: 06/19/2023]
Abstract
Inertial effects affecting both the translational and rotational dynamics are inherent to a broad range of active systems at the macroscopic scale. Thus, there is a pivotal need for proper models in the framework of active matter to correctly reproduce experimental results, hopefully achieving theoretical insights. For this purpose, we propose an inertial version of the active Ornstein-Uhlenbeck particle (AOUP) model accounting for particle mass (translational inertia) as well as its moment of inertia (rotational inertia) and derive the full expression for its steady-state properties. The inertial AOUP dynamics introduced in this paper is designed to capture the basic features of the well-established inertial active Brownian particle model, i.e. the persistence time of the active motion and the long-time diffusion coefficient. For a small or moderate rotational inertia, these two models predict similar dynamics at all timescales and, in general, our inertial AOUP model consistently yields the same trend upon changing the moment of inertia for various dynamical correlation functions.
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Affiliation(s)
- Alexander R Sprenger
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
- Institut für Physik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, D-39106 Magdeburg, Germany
| | - Lorenzo Caprini
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - René Wittmann
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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26
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Caprini L, Löwen H. Flocking without Alignment Interactions in Attractive Active Brownian Particles. PHYSICAL REVIEW LETTERS 2023; 130:148202. [PMID: 37084461 DOI: 10.1103/physrevlett.130.148202] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/24/2022] [Accepted: 03/13/2023] [Indexed: 05/03/2023]
Abstract
Within a simple model of attractive active Brownian particles, we predict flocking behavior and challenge the widespread idea that alignment interactions are necessary to observe this collective phenomenon. Here, we show that even nonaligning attractive interactions can lead to a flocking state. Monitoring the velocity polarization as the order parameter, we reveal the onset of a first-order transition from a disordered phase, characterized by several small clusters, to a flocking phase, where a single flocking cluster is emerging. The scenario is confirmed by studying the spatial connected correlation function of particle velocities, which reveals scale-free behavior in flocking states and exponential-like decay for nonflocking configurations. Our predictions can be tested in microscopic and macroscopic experiments showing flocking, such as animals, migrating cells, and active colloids.
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Affiliation(s)
- L Caprini
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - H Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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27
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Cates ME, Nardini C. Classical Nucleation Theory for Active Fluid Phase Separation. PHYSICAL REVIEW LETTERS 2023; 130:098203. [PMID: 36930897 DOI: 10.1103/physrevlett.130.098203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2022] [Accepted: 02/10/2023] [Indexed: 06/18/2023]
Abstract
Classical Nucleation Theory (CNT), linking rare nucleation events to the free-energy landscape of a growing nucleus, is central to understanding phase-change kinetics in passive fluids. Nucleation in nonequilibrium systems is much harder to describe because there is no free energy, but instead a dynamics-dependent quasipotential that typically must be found numerically. Here we extend CNT to a class of active phase-separating systems governed by a minimal field-theoretic model (Active Model B+). In the small noise and supersaturation limits that CNT assumes, we compute analytically the quasipotential, and hence, nucleation barrier, for liquid-vapor phase separation. Crucial to our results, detailed balance, although broken microscopically by activity, is restored along the instanton trajectory, which in CNT involves the nuclear radius as the sole reaction coordinate.
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Affiliation(s)
- M E Cates
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - C Nardini
- Service de Physique de l'Etat Condensé, CEA, CNRS Université Paris-Saclay, CEA-Saclay, 91191 Gif-sur-Yvette, France
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée, 75005 Paris, France
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28
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Crisanti A, Paoluzzi M. Most probable path of active Ornstein-Uhlenbeck particles. Phys Rev E 2023; 107:034110. [PMID: 37072947 DOI: 10.1103/physreve.107.034110] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2022] [Accepted: 02/17/2023] [Indexed: 04/20/2023]
Abstract
Using the path integral representation of the nonequilibrium dynamics, we compute the most probable path between arbitrary starting and final points that is followed by an active particle driven by persistent noise. We focus our attention on the case of active particles immersed in harmonic potentials, where the trajectory can be computed analytically. Once we consider the extended Markovian dynamics where the self-propulsive drive evolves according to an Ornstein-Uhlenbeck process, we can compute the trajectory analytically with arbitrary conditions on position and self-propulsion velocity. We test the analytical predictions against numerical simulations and we compare the analytical results with those obtained within approximated equilibriumlike dynamics.
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Affiliation(s)
- Andrea Crisanti
- Dipartimento di Fisica, Sapienza Università di Roma Piazzale A. Moro 2, I-00185 Rome, Italy
| | - Matteo Paoluzzi
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, C. Martí Franquès 1, 08028 Barcelona, Spain
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29
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Bao R, Hou Z. Improving estimation of entropy production rate for run-and-tumble particle systems by high-order thermodynamic uncertainty relation. Phys Rev E 2023; 107:024112. [PMID: 36932577 DOI: 10.1103/physreve.107.024112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Accepted: 01/30/2023] [Indexed: 02/12/2023]
Abstract
Entropy production plays an important role in the regulation and stability of active matter systems, and its rate quantifies the nonequilibrium nature of these systems. However, entropy production is hard to experimentally estimate even in some simple active systems like molecular motors or bacteria, which may be modeled by the run-and-tumble particle (RTP), a representative model in the study of active matters. Here we resolve this problem for an asymmetric RTP in one dimension, first constructing a finite-time thermodynamic uncertainty relation (TUR) for a RTP, which works well in the short observation time regime for entropy production estimation. Nevertheless, when the activity dominates, i.e., the RTP is far from equilibrium, the lower bound for entropy production from TUR turns out to be trivial. We address this issue by introducing a recently proposed high-order thermodynamic uncertainty relation (HTUR), in which the cumulant generating function of current serves as a key ingredient. To exploit the HTUR, we adopt a method to analytically obtain the cumulant generating function of the current we study, with no need to explicitly know the time-dependent probability distribution. The HTUR is demonstrated to be able to estimate the steady state energy dissipation rate accurately because the cumulant generating function covers higher-order statistics of the current, including rare and large fluctuations besides its variance. Compared to the conventional TUR, the HTUR could give significantly improved estimation of energy dissipation, which can work well even in the far from equilibrium regime. We also provide a strategy based on the improved bound to estimate the entropy production from a moderate amount of trajectory data for experimental feasibility.
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Affiliation(s)
- Ruicheng Bao
- Department of Chemical Physics & Hefei National Laboratory for Physical Sciences at Microscales, iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Zhonghuai Hou
- Department of Chemical Physics & Hefei National Laboratory for Physical Sciences at Microscales, iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China
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30
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Shi H, Du L, Huang F, Guo W. Weak ergodicity breaking and anomalous diffusion in collective motion of active particles under spatiotemporal disorder. Phys Rev E 2023; 107:024114. [PMID: 36932613 DOI: 10.1103/physreve.107.024114] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2021] [Accepted: 01/12/2023] [Indexed: 06/18/2023]
Abstract
The effects of spatiotemporal disorder, i.e., both the noise and quenched disorder, on the dynamics of active particles in two dimensions are investigated. We demonstrate that within the tailored parameter regime, nonergodic superdiffusion and nonergodic subdiffusion occur in the system, identified by the observable quantities (the mean squared displacement and ergodicity-breaking parameter) averaged over both the noise and realizations of quenched disorder. Their origins are attributed to the competition effects between the neighbor alignment and spatiotemporal disorder on the collective motion of active particles. These results may be helpful for further understanding the nonequilibrium transport process of active particles, as well as for detection of the transport of self-propelled particles in complex and crowded environments.
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Affiliation(s)
- Hongda Shi
- Key Laboratory of Artificial Microstructures in Yunnan Higher Education Institutions, School of Physical Science and Technology, Kunming University, Kunming 650214, China
| | - Luchun Du
- Department of Physics, Yunnan University, Kunming 650091, China
| | - Feijie Huang
- Key Laboratory of Artificial Microstructures in Yunnan Higher Education Institutions, School of Physical Science and Technology, Kunming University, Kunming 650214, China
| | - Wei Guo
- Key Laboratory of Artificial Microstructures in Yunnan Higher Education Institutions, School of Physical Science and Technology, Kunming University, Kunming 650214, China
- Yunnan Key Laboratory of Metal-Organic Molecular Materials and Devices, Kunming University, Kunming 650214, China
- National Laboratory of Solid State Microstructures, Department of Physics, Nanjing University, Nanjing 210093, China
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31
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de Souza Silva CC, Cirne D, Freitas O, Campos PRA. Phenotypic evolution as an Ornstein-Uhlenbeck process: The effect of environmental variation and phenotypic plasticity. Phys Rev E 2023; 107:024417. [PMID: 36932534 DOI: 10.1103/physreve.107.024417] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2022] [Accepted: 02/13/2023] [Indexed: 03/19/2023]
Abstract
Here we investigate phenotypic evolution from the perspective of the Ornstein-Uhlenbeck (OU) process. Evolutionarily speaking, the model assumes the existence of stabilizing selection toward a phenotypic optimum. The standard (OU) model is modified to include environmental variation by taking a moving phenotypic optimum and endowing organisms with phenotypic plasticity. These two processes lead to an effective fitness landscape, which deforms the original. We observe that the simultaneous occurrence of environmental variation and phenotypic plasticity leads to skewed phenotypic distributions. The skewness of the resulting phenotypic distributions strongly depends on the rate of environmental variation and strength of selection. When generalized to more than one trait, the phenotypic distributions are not only affected by the magnitude of the rate of environmental variation but also by its direction. A remarkable feature of our predictions is the existence of an upper bound for the critical rate of environmental variation to allow population persistence, even if there is no cost associated with phenotypic plasticity.
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Affiliation(s)
| | - Diego Cirne
- Departamento de Física, Universidade Federal de Pernambuco, 50740-560 Recife-PE, Brazil
| | - Osmar Freitas
- Departamento de Física, Universidade Federal de Pernambuco, 50740-560 Recife-PE, Brazil
| | - Paulo R A Campos
- Departamento de Física, Universidade Federal de Pernambuco, 50740-560 Recife-PE, Brazil
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32
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Sarkar R, Santra I, Basu U. Stationary states of activity-driven harmonic chains. Phys Rev E 2023; 107:014123. [PMID: 36797958 DOI: 10.1103/physreve.107.014123] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2022] [Accepted: 12/22/2022] [Indexed: 01/19/2023]
Abstract
We study the stationary state of a chain of harmonic oscillators driven by two active reservoirs at the two ends. These reservoirs exert correlated stochastic forces on the boundary oscillators which eventually leads to a nonequilibrium stationary state of the system. We consider three most well-known dynamics for the active force, namely, the active Ornstein-Uhlenbeck process, run-and-tumble process, and active Brownian process, all of which have exponentially decaying two-point temporal correlations but very different higher-order fluctuations. We show that, irrespective of the specific dynamics of the drive, the stationary velocity fluctuations are Gaussian in nature with a kinetic temperature which remains uniform in the bulk. Moreover, we find the emergence of an "equipartition of energy" in the bulk of the system-the bulk kinetic temperature equals the bulk potential temperature in the thermodynamic limit. We also calculate the stationary distribution of the instantaneous energy current in the bulk which always shows a logarithmic divergence near the origin and asymmetric exponential tails. The signatures of specific active driving become visible in the behavior of the oscillators near the boundary. This is most prominent for the RTP- and ABP-driven chains where the boundary velocity distributions become non-Gaussian and the current distribution has a finite cutoff.
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Affiliation(s)
- Ritwick Sarkar
- S. N. Bose National Centre for Basic Sciences, Kolkata 700106, India
| | - Ion Santra
- Raman Research Institute, Bengaluru 560080, India
| | - Urna Basu
- S. N. Bose National Centre for Basic Sciences, Kolkata 700106, India.,Raman Research Institute, Bengaluru 560080, India
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33
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Frydel D. Entropy production of active particles formulated for underdamped dynamics. Phys Rev E 2023; 107:014604. [PMID: 36797961 DOI: 10.1103/physreve.107.014604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2022] [Accepted: 01/03/2023] [Indexed: 06/18/2023]
Abstract
The present work investigates the effect of inertia on the entropy production rate Π for all canonical models of active particles for different dimensions and the type of confinement. To calculate Π, the link between the entropy production and dissipation of heat rate is explored, resulting in a simple and intuitive expression. By analyzing the Kramers equation, alternative formulations of Π are obtained and the virial theorem for active particles is derived. Exact results are obtained for particles in an unconfined environment and in a harmonic trap. In both cases, Π is independent of temperature. For the case of a harmonic trap, Π attains a maximal value for τ=ω^{-1}, where τ is the persistence time and ω is the natural frequency of an oscillator. For active particles in one-dimensional box, or other nonharmonic potentials, thermal fluctuations are found to reduce Π.
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Affiliation(s)
- Derek Frydel
- Department of Chemistry, Universidad Técnica Federico Santa María, Campus San Joaquin, 7820275 Santiago, Chile
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34
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Padmanabha P, Busiello DM, Maritan A, Gupta D. Fluctuations of entropy production of a run-and-tumble particle. Phys Rev E 2023; 107:014129. [PMID: 36797901 DOI: 10.1103/physreve.107.014129] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2022] [Accepted: 12/22/2022] [Indexed: 06/18/2023]
Abstract
Out-of-equilibrium systems continuously generate entropy, with its rate of production being a fingerprint of nonequilibrium conditions. In small-scale dissipative systems subject to thermal noise, fluctuations of entropy production are significant. Hitherto, mean and variance have been abundantly studied, even if higher moments might be important to fully characterize the system of interest. Here, we introduce a graphical method to compute any moment of entropy production for a generic discrete-state system. Then, we focus on a paradigmatic model of active particles, i.e., run-and-tumble dynamics, which resembles the motion observed in several micro-organisms. Employing our framework, we compute the first three cumulants of the entropy production for a discrete version of this model. We also compare our analytical results with numerical simulations. We find that as the number of states increases, the distribution of entropy production deviates from a Gaussian. Finally, we extend our framework to a continuous state-space run-and-tumble model, using an appropriate scaling of the transition rates. The approach presented here might help uncover the features of nonequilibrium fluctuations of any current in biological systems operating out-of-equilibrium.
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Affiliation(s)
- Prajwal Padmanabha
- Department of Physics and Astronomy "G. Galilei," University of Padova, Padova 35131, Italy
| | | | - Amos Maritan
- Department of Physics and Astronomy "G. Galilei," University of Padova, Padova 35131, Italy
| | - Deepak Gupta
- Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
- Institute for Theoretical Physics, Technical University of Berlin, Hardenbergstrasse 36, D-10623 Berlin, Germany
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35
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Te Vrugt M, Wittkowski R. Perspective: New directions in dynamical density functional theory. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 35:041501. [PMID: 35917827 DOI: 10.1088/1361-648x/ac8633] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2022] [Accepted: 08/01/2022] [Indexed: 06/15/2023]
Abstract
Classical dynamical density functional theory (DDFT) has become one of the central modeling approaches in nonequilibrium soft matter physics. Recent years have seen the emergence of novel and interesting fields of application for DDFT. In particular, there has been a remarkable growth in the amount of work related to chemistry. Moreover, DDFT has stimulated research on other theories such as phase field crystal models and power functional theory. In this perspective, we summarize the latest developments in the field of DDFT and discuss a variety of possible directions for future research.
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Affiliation(s)
- Michael Te Vrugt
- Institut für Theoretische Physik, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany
| | - Raphael Wittkowski
- Institut für Theoretische Physik, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany
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36
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Banerjee T, Jack RL, Cates ME. Role of initial conditions in one-dimensional diffusive systems: Compressibility, hyperuniformity, and long-term memory. Phys Rev E 2022; 106:L062101. [PMID: 36671167 DOI: 10.1103/physreve.106.l062101] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2022] [Accepted: 11/04/2022] [Indexed: 06/17/2023]
Abstract
We analyze the long-lasting effects of initial conditions on dynamical fluctuations in one-dimensional diffusive systems. We consider the mean-squared displacement of tracers in homogeneous systems with single-file diffusion, and current fluctuations for noninteracting diffusive particles. In each case we show analytically that the long-term memory of initial conditions is mediated by a single static quantity: a generalized compressibility that quantifies the density fluctuations of the initial state. We thereby identify a universality class of hyperuniform initial states whose dynamical variances coincide with the quenched cases studied previously, alongside a continuous family of other classes among which equilibrated (or annealed) initial conditions are but one member. We verify our predictions through extensive Monte Carlo simulations.
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Affiliation(s)
- Tirthankar Banerjee
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Robert L Jack
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Michael E Cates
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
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37
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Ro S, Guo B, Shih A, Phan TV, Austin RH, Levine D, Chaikin PM, Martiniani S. Model-Free Measurement of Local Entropy Production and Extractable Work in Active Matter. PHYSICAL REVIEW LETTERS 2022; 129:220601. [PMID: 36493452 DOI: 10.1103/physrevlett.129.220601] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/22/2022] [Accepted: 09/09/2022] [Indexed: 06/17/2023]
Abstract
Time-reversal symmetry breaking and entropy production are universal features of nonequilibrium phenomena. Despite its importance in the physics of active and living systems, the entropy production of systems with many degrees of freedom has remained of little practical significance because the high dimensionality of their state space makes it difficult to measure. Here we introduce a local measure of entropy production and a numerical protocol to estimate it. We establish a connection between the entropy production and extractability of work in a given region of the system and show how this quantity depends crucially on the degrees of freedom being tracked. We validate our approach in theory, simulation, and experiments by considering systems of active Brownian particles undergoing motility-induced phase separation, as well as active Brownian particles and E.coli in a rectifying device in which the time-reversal asymmetry of the particle dynamics couples to spatial asymmetry to reveal its effects on a macroscopic scale.
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Affiliation(s)
- Sunghan Ro
- Department of Physics, Technion-Israel Institute of Technology, Haifa 3200003, Israel
| | - Buming Guo
- Center for Soft Matter Research, Department of Physics, New York University, New York 10003, USA
| | - Aaron Shih
- Center for Soft Matter Research, Department of Physics, New York University, New York 10003, USA
- Courant Institute of Mathematical Sciences, New York University, New York 10003, USA
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Trung V Phan
- Department of Physics, Princeton University, Princeton 08544, New Jersey, USA
| | - Robert H Austin
- Department of Physics, Princeton University, Princeton 08544, New Jersey, USA
| | - Dov Levine
- Department of Physics, Technion-Israel Institute of Technology, Haifa 3200003, Israel
| | - Paul M Chaikin
- Center for Soft Matter Research, Department of Physics, New York University, New York 10003, USA
| | - Stefano Martiniani
- Center for Soft Matter Research, Department of Physics, New York University, New York 10003, USA
- Courant Institute of Mathematical Sciences, New York University, New York 10003, USA
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
- Simons Center for Computational Physical Chemistry, Department of Chemistry, New York University, New York 10003, USA
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38
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Goerlich R, Pires LB, Manfredi G, Hervieux PA, Genet C. Harvesting information to control nonequilibrium states of active matter. Phys Rev E 2022; 106:054617. [PMID: 36559455 DOI: 10.1103/physreve.106.054617] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2021] [Accepted: 11/02/2022] [Indexed: 06/17/2023]
Abstract
We propose to use a correlated noise bath to drive an optically trapped Brownian particle that mimics active biological matter. Due to the flexibility and precision of our setup, we are able to control the different parameters that drive the stochastic motion of the particle with unprecedented accuracy, thus reaching strongly correlated regimes that are not easily accessible with real active matter. In particular, by using the correlation time (i.e., the "color") of the noise as a control parameter, we can trigger transitions between two nonequilibrium steady states with no expended work, but only a calorific cost. Remarkably, the measured heat production is directly proportional to the spectral entropy of the correlated noise, in a fashion that is reminiscent of Landauer's principle. Our procedure can be viewed as a method for harvesting information from the active fluctuations.
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Affiliation(s)
- Rémi Goerlich
- Université de Strasbourg, CNRS, Institut de Physique et Chimie des Matériaux de Strasbourg, UMR 7504, F-67000 Strasbourg, France
- Université de Strasbourg, CNRS, Institut de Science et d'Ingénierie Supramoléculaires, UMR 7006, F-67000 Strasbourg, France
| | - Luís Barbosa Pires
- Université de Strasbourg, CNRS, Institut de Science et d'Ingénierie Supramoléculaires, UMR 7006, F-67000 Strasbourg, France
| | - Giovanni Manfredi
- Université de Strasbourg, CNRS, Institut de Physique et Chimie des Matériaux de Strasbourg, UMR 7504, F-67000 Strasbourg, France
| | - Paul-Antoine Hervieux
- Université de Strasbourg, CNRS, Institut de Physique et Chimie des Matériaux de Strasbourg, UMR 7504, F-67000 Strasbourg, France
| | - Cyriaque Genet
- Université de Strasbourg, CNRS, Institut de Science et d'Ingénierie Supramoléculaires, UMR 7006, F-67000 Strasbourg, France
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39
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Gnan N, Maggi C. Critical behavior of quorum-sensing active particles. SOFT MATTER 2022; 18:7654-7661. [PMID: 36169619 DOI: 10.1039/d2sm00654e] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
It is still a debated issue whether all critical active particles belong to the same universality class. Here we numerically study the critical behavior of quorum sensing active particles that represents the archetypal model for interpreting motility-induced phase separation. Mean-field theory predicts that this model should undergo a full phase separation if particles slow-down enough when sensing the presence of their neighbors and that the coexistence line terminates in a critical point. By performing large-scale numerical simulations, we confirm this scenario, locate the critical point and use finite-size scaling analysis to show that the static and dynamic critical exponents of this active system substantially agree with those of the Ising universality class.
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Affiliation(s)
- Nicoletta Gnan
- ISC-CNR, Institute for Complex Systems, Piazzale A. Moro 2, I-00185, Roma, Italy.
- Dipartimento di Fisica, Università di Roma "Sapienza", I-00185, Roma, Italy
| | - Claudio Maggi
- Dipartimento di Fisica, Università di Roma "Sapienza", I-00185, Roma, Italy
- NANOTEC-CNR, Institute of Nanotechnology, Soft and Living Matter Laboratory-Piazzale A. Moro 2, I-00185, Roma, Italy.
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40
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Ferretti F, Grosse-Holz S, Holmes C, Shivers JL, Giardina I, Mora T, Walczak AM. Signatures of irreversibility in microscopic models of flocking. Phys Rev E 2022; 106:034608. [PMID: 36266796 DOI: 10.1103/physreve.106.034608] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2022] [Accepted: 08/17/2022] [Indexed: 06/16/2023]
Abstract
Flocking in d=2 is a genuine nonequilibrium phenomenon for which irreversibility is an essential ingredient. We study a class of minimal flocking models whose only source of irreversibility is self-propulsion and use the entropy production rate (EPR) to quantify the departure from equilibrium across their phase diagrams. The EPR is maximal in the vicinity of the order-disorder transition, where reshuffling of the interaction network is fast. We show that signatures of irreversibility come in the form of asymmetries in the steady-state distribution of the flock's microstates. These asymmetries occur as consequences of the time-reversal symmetry breaking in the considered self-propelled systems, independently of the interaction details. In the case of metric pairwise forces, they reduce to local asymmetries in the distribution of pairs of particles. This study suggests a possible use of pair asymmetries both to quantify the departure from equilibrium and to learn relevant information about aligning interaction potentials from data.
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Affiliation(s)
- Federica Ferretti
- Dipartimento di Fisica, Università Sapienza, 00185 Rome, Italy
- Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, UOS Sapienza, 00185 Rome, Italy
| | - Simon Grosse-Holz
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Institut Curie, Paris 75005, France
| | - Caroline Holmes
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Jordan L Shivers
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, USA
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77030, USA
| | - Irene Giardina
- Dipartimento di Fisica, Università Sapienza, 00185 Rome, Italy
- Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, UOS Sapienza, 00185 Rome, Italy
- INFN, Unità di Roma 1, 00185 Rome, Italy
| | - Thierry Mora
- Laboratoire de Physique de l'École Normale Supérieure (PSL University), CNRS, Sorbonne Université, Université de Paris, 75005 Paris, France
| | - Aleksandra M Walczak
- Laboratoire de Physique de l'École Normale Supérieure (PSL University), CNRS, Sorbonne Université, Université de Paris, 75005 Paris, France
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41
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Williams S, Jeanneret R, Tuval I, Polin M. Confinement-induced accumulation and de-mixing of microscopic active-passive mixtures. Nat Commun 2022; 13:4776. [PMID: 35970896 PMCID: PMC9378696 DOI: 10.1038/s41467-022-32520-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2022] [Accepted: 08/03/2022] [Indexed: 11/13/2022] Open
Abstract
Understanding the out-of-equilibrium properties of noisy microscale systems and the extent to which they can be modulated externally, is a crucial scientific and technological challenge. It holds the promise to unlock disruptive new technologies ranging from targeted delivery of chemicals within the body to directed assembly of new materials. Here we focus on how active matter can be harnessed to transport passive microscopic systems in a statistically predictable way. Using a minimal active-passive system of weakly Brownian particles and swimming microalgae, we show that spatial confinement leads to a complex non-monotonic steady-state distribution of colloids, with a pronounced peak at the boundary. The particles’ emergent active dynamics is well captured by a space-dependent Poisson process resulting from the space-dependent motion of the algae. Based on our findings, we then realise experimentally the de-mixing of the active-passive suspension, opening the way for manipulating colloidal objects via controlled activity fields. Understanding how order emerges in active matter may facilitate macroscopic control of microscopic objects. Here, Williams et al. show how to control the transport of passive microscopic particles in presence of motile algae in conjunction with boundary-induced accumulation of microswimmers.
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Affiliation(s)
- Stephen Williams
- Department of Physics, University of Warwick, Coventry, CV4 7AL, United Kingdom
| | - Raphaël Jeanneret
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005, Paris, France
| | - Idan Tuval
- Departament de Física, Universitat de les Illes Balears, 07071, Palma de Mallorca, Spain.,Instituto Mediterráneo de Estudios Avanzados, IMEDEA, Miquel Marques 21, 07190, Esporles, Spain
| | - Marco Polin
- Department of Physics, University of Warwick, Coventry, CV4 7AL, United Kingdom. .,Departament de Física, Universitat de les Illes Balears, 07071, Palma de Mallorca, Spain. .,Instituto Mediterráneo de Estudios Avanzados, IMEDEA, Miquel Marques 21, 07190, Esporles, Spain.
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42
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Muhsin M, Sahoo M. Inertial active Ornstein-Uhlenbeck particle in the presence of a magnetic field. Phys Rev E 2022; 106:014605. [PMID: 35974582 DOI: 10.1103/physreve.106.014605] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2022] [Accepted: 06/29/2022] [Indexed: 06/15/2023]
Abstract
We consider an inertial active Ornstein-Uhlenbeck particle in an athermal bath. The particle is charged, constrained to move in a two-dimensional harmonic trap, and a magnetic field is applied perpendicular to the plane of motion. The steady-state correlations and the mean-square displacement are studied when the particle is confined as well as when it is set free from the trap. With the help of both numerical simulation and analytical calculations, we observe that inertia plays a crucial role in the dynamics in the presence of a magnetic field. In a highly viscous medium where the inertial effects are negligible, the magnetic field has no influence on the correlated behavior of position as well as velocity. In the time asymptotic limit, the overall displacement of the confined harmonic particle gets enhanced by the presence of a magnetic field and saturates for a stronger magnetic field. On the other hand, when the particle is set free, the overall displacement gets suppressed and approaches zero when the strength of the field is very high. Interestingly, it is seen that in the time asymptotic limit, the confined harmonic particle behaves like a passive particle and becomes independent of the activity, especially in the presence of a very strong magnetic field. Similarly, for a free particle the mean-square displacement in the long time limit becomes independent of activity even for a longer persistence of noise cor- relation in the dynamics.
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Affiliation(s)
- M Muhsin
- Department of Physics, University of Kerala, Kariavattom, Thiruvananthapuram 695581, India
| | - M Sahoo
- Department of Physics, University of Kerala, Kariavattom, Thiruvananthapuram 695581, India
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43
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Yan J, Rotskoff G. Physics-informed graph neural networks enhance scalability of variational nonequilibrium optimal control. J Chem Phys 2022; 157:074101. [DOI: 10.1063/5.0095593] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
When a physical system is driven away from equilibrium, the statistical distribution of its dynamical trajectories informs many of its physical properties. Characterizing the nature of the distribution of dynamical observables, such as a current or entropy production rate, has become a central problem in nonequilibrium statistical mechanics. Asymptotically, for a broad class of observables, the distribution of a given observable satisfies a large deviation principle when the dynamics is Markovian, meaning that fluctuations can be characterized in the long-time limit by computing a scaled cumulant generating function. Calculating this function is not tractable analytically (nor often numerically) for complex, interacting systems, so the development of robust numerical techniques to carry out this computation is needed to probe the properties of nonequilibrium materials. Here, we describe an algorithm that recasts this task as an optimal control problem that can be solved variationally. We solve for optimal control forces using neural network ansätze that are tailored to the physical systems to which the forces are applied. We demonstrate that this approach leads to transferable and accurate solutions in two systems featuring large numbers of interacting particles.
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Affiliation(s)
- Jiawei Yan
- Stanford University Department of Chemistry, United States of America
| | - Grant Rotskoff
- Chemistry, Stanford University Department of Chemistry, United States of America
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44
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Cockrell C, Ford IJ. Stochastic thermodynamics in a non-Markovian dynamical system. Phys Rev E 2022; 105:064124. [PMID: 35854505 DOI: 10.1103/physreve.105.064124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2022] [Accepted: 06/02/2022] [Indexed: 06/15/2023]
Abstract
The developing field of stochastic thermodynamics extends concepts of macroscopic thermodynamics such as entropy production and work to the microscopic level of individual trajectories taken by a system through phase space. The scheme involves coupling the system to an environment-typically a source of Markovian noise that affects the dynamics of the system. Here we extend this framework to consider a non-Markovian environment, one whose dynamics have memory and which create additional correlations with the system variables, and illustrate this with a selection of simple examples. Such an environment produces a rich variety of behavior. In particular, for a case of thermal relaxation, the distributions of entropy produced under the non-Markovian dynamics differ from the equivalent case of Markovian dynamics only by a delay time. When a time-dependent external work protocol is turned on, the system's correlations with the environment can either assist or hinder its approach to equilibrium, and affect its production of entropy, depending on the coupling strength between the system and environment.
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Affiliation(s)
- Cillian Cockrell
- School of Physical and Chemical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
| | - Ian J Ford
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
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45
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C P S, Joy A. Effective temperature and Einstein relation for particles in active matter flows. Phys Rev E 2022; 105:065114. [PMID: 35854616 DOI: 10.1103/physreve.105.065114] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2021] [Accepted: 06/09/2022] [Indexed: 06/15/2023]
Abstract
Active matter are a collection of units with intrinsic supply of energy that is utilized for self-propelled motion. Recent studies have confirmed that these active systems can exist in exotic phases, such as swarming, laning, jamming, and even turbulence, based on the size and density of the constituent units. An interesting question that naturally arises is whether one can identify an effective temperature for particles advected by such an active flow that is far from equilibrium. In this paper, we report using a continuum model of a dense bacterial suspension, an exact expression of the effective temperature for a distribution of interacting particles that are immersed in this suspension. We observe that this effective temperature is linear in particle diffusivity with the slope defining the particle mobility that is higher when the background fluid exhibits global polar ordering and lower when the fluid is in isotropic equilibrium. We believe our paper is a direct verification of the Einstein relation-the simplest fluctuation dissipation relation for interacting particles advected in an active matter flow.
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Affiliation(s)
- Sanjay C P
- Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India
| | - Ashwin Joy
- Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India
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46
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Lisin EA, Vaulina OS, Lisina II, Petrov OF. Motion of a self-propelled particle with rotational inertia. Phys Chem Chem Phys 2022; 24:14150-14158. [PMID: 35648110 DOI: 10.1039/d2cp01313d] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Overdamped active Brownian motion of self-propelled particles in a liquid has been fairly well studied. However, there are a variety of situations in which the overdamped approximation is not justified, for instance, when self-propelled particles move in a low-viscosity medium or when their rotational diffusivity is enhanced by internal active processes or external control. Examples of various origins include biofilaments driven by molecular motors, living and artificial microflyers and interfacial surfers, field-controlled and superfluid microswimmers, vibration-driven granular particles and autonomous mini-robots with sensorial delays, etc. All of them extend active Brownian motion to the underdamped case, i.e., to active Langevin motion, which takes into account inertia. Despite a rich experimental background, there is a gap in the theory in the field where rotational inertia significantly affects the random walk of active particles on all time scales. In particular, although the well-known models of active Brownian and Ornstein-Uhlenbeck particles include a memory effect of the direction of motion, they are not applicable in the underdamped case, because the rotational inertia, which they do not account for, can partially prevent "memory loss" with increasing rotational diffusion. We describe the two-dimensional motion of a self-propelled particle with both translational and rotational inertia and velocity fluctuations. The proposed generalized analytical equations for the mean kinetic energy, mean-square displacement and noise-averaged trajectory of the self-propelled particle are confirmed by numerical simulations in a wide range of self-propulsion velocities, moments of inertia, rotational diffusivities, medium viscosities and observation times.
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Affiliation(s)
- E A Lisin
- Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, 125412, Russia.
| | - O S Vaulina
- Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, 125412, Russia.
| | - I I Lisina
- Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, 125412, Russia.
| | - O F Petrov
- Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, 125412, Russia.
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Speck T. Critical behavior of active Brownian particles: Connection to field theories. Phys Rev E 2022; 105:064601. [PMID: 35854575 DOI: 10.1103/physreve.105.064601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2022] [Accepted: 05/12/2022] [Indexed: 06/15/2023]
Abstract
We explore the relation between active Brownian particles, a minimal particle-based model for active matter, and scalar field theories. Both show a liquid-gas-like phase transition toward stable coexistence of a dense liquid with a dilute active gas that terminates in a critical point. However, a comprehensive mapping between the particle-based model parameters and the effective coefficients governing the field theories has not been established yet. We discuss conflicting recent numerical results for the critical exponents of active Brownian particles in two dimensions. Starting from the intermediate effective hydrodynamic equations, we then present a construction for a scalar order parameter for active Brownian particles that yields the active model B+. We argue that a crucial ingredient is the coupling between density and polarization in the particle current. The renormalization flow close to two dimensions exhibits a pair of perturbative fixed points that limit the attractive basin of the Wilson-Fisher fixed point, with the perspective that the critical behavior of active Brownian particles in two dimensions is governed by a strong-coupling fixed point different from Wilson-Fisher and not necessarily corresponding to Ising universality.
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Affiliation(s)
- Thomas Speck
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
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48
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Goswami K. Inertial particle under active fluctuations: Diffusion and work distributions. Phys Rev E 2022; 105:044123. [PMID: 35590542 DOI: 10.1103/physreve.105.044123] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2021] [Accepted: 03/30/2022] [Indexed: 06/15/2023]
Abstract
We study the underdamped motion of a passive particle in an active environment. Using the phase space path integral method we find the probability distribution function of position and velocity for a free and a harmonically bound particle. The environment is characterized by an active noise which is described as the Ornstein-Uhlenbeck process (OUP). Taking two similar, yet slightly different OUP models, it is shown how inertia along with other relevant parameters affect the dynamics of the particle. Further we investigate the work fluctuations of a harmonically trapped particle by considering the trap center being pulled at a constant speed. Finally, the fluctuation theorem of work is validated with an effective temperature in the steady-state limit.
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Affiliation(s)
- Koushik Goswami
- Department of Chemistry, Indian Institute of Technology Bombay, Mumbai, Powai 400076, India and Institute of Physics & Astronomy, University of Potsdam, Karl-Liebknecht-Straße 24/25, 14476 Potsdam-Golm, Germany
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49
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Ben Dor Y, Ro S, Kafri Y, Kardar M, Tailleur J. Disordered boundaries destroy bulk phase separation in scalar active matter. Phys Rev E 2022; 105:044603. [PMID: 35590561 DOI: 10.1103/physreve.105.044603] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2021] [Accepted: 01/11/2022] [Indexed: 06/15/2023]
Abstract
We show that disordered boundaries destroy bulk phase separation in scalar active systems in dimension d<d_{c}=3. This is in strong contrast with the equilibrium case where boundaries have no impact on the bulk of phase-separated systems. The underlying mechanism is revealed by considering a localized deformation of an otherwise flat wall, from which the case of a disordered boundary can be inferred. We find long-ranged correlations of the density field as well as a cascade of eddies which we show prevent bulk phase separation in low enough dimensions. The results are derived for dilute systems as well as in the presence of interactions, under the sole condition that the density field is the unique hydrodynamic mode. Our theoretical calculations are validated by numerical simulations of microscopic active systems.
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Affiliation(s)
- Ydan Ben Dor
- Department of Physics, Technion-Israel Institute of Technology, Haifa 3200003, Israel
| | - Sunghan Ro
- Department of Physics, Technion-Israel Institute of Technology, Haifa 3200003, Israel
| | - Yariv Kafri
- Department of Physics, Technion-Israel Institute of Technology, Haifa 3200003, Israel
| | - Mehran Kardar
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Julien Tailleur
- Université de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France
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Bhattacharya K, Chakraborty A. Aggregation of self-propelled particles with sensitivity to local order. Phys Rev E 2022; 105:044124. [PMID: 35590585 DOI: 10.1103/physreve.105.044124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2021] [Accepted: 03/16/2022] [Indexed: 06/15/2023]
Abstract
We study a system of self-propelled particles (SPPs) in which individual particles are allowed to switch between a fast aligning and a slow nonaligning state depending upon the degree of the alignment in the neighborhood. The switching is modeled using a threshold for the local order parameter. This additional attribute gives rise to a mixed phase, in contrast to the ordered phases found in clean SPP systems. As the threshold is increased from zero, we find the sudden appearance of clusters of nonaligners. Clusters of nonaligners coexist with moving clusters of aligners with continual coalescence and fragmentation. The behavior of the system with respect to the clustering of nonaligners appears to be very different for values of low and high global densities. In the low density regime, for an optimal value of the threshold, the largest cluster of nonaligners grows in size up to a maximum that varies logarithmically with the total number of particles. However, on further increasing the threshold the size decreases. In contrast, for the high density regime, an initial abrupt rise is followed by the appearance of a giant cluster of nonaligners. The latter growth can be characterized as a continuous percolation transition. In addition, we find that the speed differences between aligners and nonaligners is necessary for the segregation of aligners and nonaligners.
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Affiliation(s)
- Kunal Bhattacharya
- Department of Industrial Engineering and Management, Aalto University School of Science, 00076 Aalto, Finland
- Department of Computer Science, Aalto University School of Science, 00076 Aalto, Finland
| | - Abhijit Chakraborty
- Complexity Science Hub Vienna, Josefstaedter Strasse 39, 1080 Vienna, Austria
- Graduate School of Advanced Integrated Studies in Human Survivability, Kyoto University, 1 Nakaadachi-cho, Yoshida, Sakyo-ku, Kyoto 606-8306, Japan
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