1
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Mukherjee S, Smith NR. Large deviations in statistics of the convex hull of passive and active particles: A theoretical study. Phys Rev E 2024; 109:044120. [PMID: 38755832 DOI: 10.1103/physreve.109.044120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2023] [Accepted: 03/08/2024] [Indexed: 05/18/2024]
Abstract
We investigate analytically the distribution tails of the area A and perimeter L of a convex hull for different types of planar random walks. For N noninteracting Brownian motions of duration T we find that the large-L and -A tails behave as P(L)∼e^{-b_{N}L^{2}/DT} and P(A)∼e^{-c_{N}A/DT}, while the small-L and -A tails behave as P(L)∼e^{-d_{N}DT/L^{2}} and P(A)∼e^{-e_{N}DT/A}, where D is the diffusion coefficient. We calculated all of the coefficients (b_{N},c_{N},d_{N},e_{N}) exactly. Strikingly, we find that b_{N} and c_{N} are independent of N for N≥3 and N≥4, respectively. We find that the large-L (A) tails are dominated by a single, most probable realization that attains the desired L (A). The left tails are dominated by the survival probability of the particles inside a circle of appropriate size. For active particles and at long times, we find that large-L and -A tails are given by P(L)∼e^{-TΨ_{N}^{per}(L/T)} and P(A)∼e^{-TΨ_{N}^{area}(sqrt[A]/T)}, respectively. We calculate the rate functions Ψ_{N} exactly and find that they exhibit multiple singularities. We interpret these as DPTs of first order. We extended several of these results to dimensions d>2. Our analytic predictions display excellent agreement with existing results that were obtained from extensive numerical simulations.
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Affiliation(s)
- Soheli Mukherjee
- Department of Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, 8499000, Israel
| | - Naftali R Smith
- Department of Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, 8499000, Israel
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2
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Alston H, Cocconi L, Bertrand T. Irreversibility across a Nonreciprocal PT-Symmetry-Breaking Phase Transition. PHYSICAL REVIEW LETTERS 2023; 131:258301. [PMID: 38181344 DOI: 10.1103/physrevlett.131.258301] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2023] [Accepted: 10/30/2023] [Indexed: 01/07/2024]
Abstract
Nonreciprocal interactions are commonplace in continuum-level descriptions of both biological and synthetic active matter, yet studies addressing their implications for time reversibility have so far been limited to microscopic models. Here, we derive a general expression for the average rate of informational entropy production in the most generic mixture of conserved phase fields with nonreciprocal couplings and additive conservative noise. For the particular case of a binary system with Cahn-Hilliard dynamics augmented by nonreciprocal cross-diffusion terms, we observe a nontrivial scaling of the entropy production rate across a parity-time symmetry breaking phase transition. We derive a closed-form analytic expression in the weak-noise regime for the entropy production rate due to the emergence of a macroscopic dynamic phase, showing it can be written in terms of the global polar order parameter, a measure of parity-time symmetry breaking.
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Affiliation(s)
- Henry Alston
- Department of Mathematics, Imperial College London, South Kensington, London SW7 2AZ, United Kingdom
| | - Luca Cocconi
- Department of Mathematics, Imperial College London, South Kensington, London SW7 2AZ, United Kingdom
- The Francis Crick Institute, London NW1 1AT, United Kingdom
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany
| | - Thibault Bertrand
- Department of Mathematics, Imperial College London, South Kensington, London SW7 2AZ, United Kingdom
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3
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Kedia H, Pan D, Slotine JJ, England JL. Drive-specific selection in multistable mechanical networks. J Chem Phys 2023; 159:214106. [PMID: 38047510 DOI: 10.1063/5.0171993] [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: 11/05/2023] [Indexed: 12/05/2023] Open
Abstract
Systems with many stable configurations abound in nature, both in living and inanimate matter, encoding a rich variety of behaviors. In equilibrium, a multistable system is more likely to be found in configurations with lower energy, but the presence of an external drive can alter the relative stability of different configurations in unexpected ways. Living systems are examples par excellence of metastable nonequilibrium attractors whose structure and stability are highly dependent on the specific form and pattern of the energy flow sustaining them. Taking this distinctively lifelike behavior as inspiration, we sought to investigate the more general physical phenomenon of drive-specific selection in nonequilibrium dynamics. To do so, we numerically studied driven disordered mechanical networks of bistable springs possessing a vast number of stable configurations arising from the two stable rest lengths of each spring, thereby capturing the essential physical properties of a broad class of multistable systems. We found that there exists a range of forcing amplitudes for which the attractor states of driven disordered multistable mechanical networks are fine-tuned with respect to the pattern of external forcing to have low energy absorption from it. Additionally, we found that these drive-specific attractor states are further stabilized by precise matching between the multidimensional shape of their orbit and that of the potential energy well they inhabit. Lastly, we showed evidence of drive-specific selection in an experimental system and proposed a general method to estimate the range of drive amplitudes for drive-specific selection.
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Affiliation(s)
- Hridesh Kedia
- Physics of Living Systems Group, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Deng Pan
- Physics of Living Systems Group, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Jean-Jacques Slotine
- Nonlinear Systems Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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4
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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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5
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Baldovin M, Guéry-Odelin D, Trizac E. Control of Active Brownian Particles: An Exact Solution. PHYSICAL REVIEW LETTERS 2023; 131:118302. [PMID: 37774311 DOI: 10.1103/physrevlett.131.118302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2022] [Revised: 07/17/2023] [Accepted: 08/15/2023] [Indexed: 10/01/2023]
Abstract
Control of stochastic systems is a challenging open problem in statistical physics, with a wealth of potential applications from biology to granulates. Unlike most cases investigated so far, we aim here at controlling a genuinely out-of-equilibrium system, the two dimensional active Brownian particles model in a harmonic potential, a paradigm for the study of self-propelled bacteria. We search for protocols for the driving parameters (stiffness of the potential and activity of the particles) bringing the system from an initial passivelike steady state to a final activelike one, within a chosen time interval. The exact analytical results found for this prototypical model of self-propelled particles brings control techniques to a wider class of out-of-equilibrium systems.
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Affiliation(s)
- Marco Baldovin
- Université Paris-Saclay, CNRS, LPTMS, 91405, Orsay, France
- Institute for Complex Systems, CNR, 00185, Rome, Italy
| | - David Guéry-Odelin
- Université Paul Sabatier-Toulouse 3, CNRS, LCAR, 31062 Toulouse Cedex 9, France
| | - Emmanuel Trizac
- Université Paris-Saclay, CNRS, LPTMS, 91405, Orsay, France
- Ecole normale supérieure de Lyon, F-69342 Lyon, France
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6
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Oh Y, Baek Y. Effects of the self-propulsion parity on the efficiency of a fuel-consuming active heat engine. Phys Rev E 2023; 108:024602. [PMID: 37723679 DOI: 10.1103/physreve.108.024602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2023] [Accepted: 06/21/2023] [Indexed: 09/20/2023]
Abstract
We propose a thermodynamically consistent, analytically tractable model of steady-state active heat engines driven by both temperature difference and a constant chemical driving. While the engine follows the dynamics of the active Ornstein-Uhlenbeck particle, its self-propulsion stems from the mechanochemical coupling with the fuel consumption dynamics, allowing for both even- and odd-parity self-propulsion forces. Using the standard methods of stochastic thermodynamics, we show that the entropy production of the engine satisfies the conventional Clausius relation, based on which we define the efficiency of the model that is bounded from above by the second law of thermodynamics. Using this framework, we obtain exact expressions for the efficiency at maximum power. The results show that the engine performance has a nonmonotonic dependence on the magnitude of the chemical driving and that the even-parity (odd-parity) engines perform better when the size of the engine is smaller (larger) than the persistence length of the active particle. We also discuss the existence of a tighter upper bound on the efficiency of the odd-parity engines stemming from the detailed structure of the entropy production.
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Affiliation(s)
- Yongjae Oh
- Department of Physics and Astronomy & Center for Theoretical Physics, Seoul National University, Seoul 08826, Republic of Korea
| | - Yongjoo Baek
- Department of Physics and Astronomy & Center for Theoretical Physics, Seoul National University, Seoul 08826, Republic of Korea
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7
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Agranov T, Cates ME, Jack RL. Tricritical Behavior in Dynamical Phase Transitions. PHYSICAL REVIEW LETTERS 2023; 131:017102. [PMID: 37478424 DOI: 10.1103/physrevlett.131.017102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2022] [Revised: 03/31/2023] [Accepted: 05/23/2023] [Indexed: 07/23/2023]
Abstract
We identify a new scenario for dynamical phase transitions associated with time-integrated observables occurring in diffusive systems described by the macroscopic fluctuation theory. It is characterized by the pairwise meeting of first- and second-order bias-induced phase transition curves at two tricritical points. We formulate a simple, general criterion for its appearance and derive an exact Landau theory for the tricritical behavior. The scenario is demonstrated in three examples: the simple symmetric exclusion process biased by an activity-related structural observable; the Katz-Lebowitz-Spohn lattice gas model biased by its current; and in an active lattice gas biased by its entropy production.
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Affiliation(s)
- Tal Agranov
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, United Kingdom
| | - Michael E Cates
- 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
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8
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Hurtado-Gutiérrez R, Hurtado PI, Pérez-Espigares C. Spectral signatures of symmetry-breaking dynamical phase transitions. Phys Rev E 2023; 108:014107. [PMID: 37583207 DOI: 10.1103/physreve.108.014107] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2023] [Accepted: 06/12/2023] [Indexed: 08/17/2023]
Abstract
Large deviation theory provides the framework to study the probability of rare fluctuations of time-averaged observables, opening new avenues of research in nonequilibrium physics. Some of the most appealing results within this context are dynamical phase transitions (DPTs), which might occur at the level of trajectories in order to maximize the probability of sustaining a rare event. While macroscopic fluctuation theory has underpinned much recent progress on the understanding of symmetry-breaking DPTs in driven diffusive systems, their microscopic characterization is still challenging. In this work we shed light on the general spectral mechanism giving rise to continuous DPTs not only for driven diffusive systems, but for any jump process in which a discrete Z_{n} symmetry is broken. By means of a symmetry-aided spectral analysis of the Doob-transformed dynamics, we provide the conditions whereby symmetry-breaking DPTs might emerge and how the different dynamical phases arise from the specific structure of the degenerate eigenvectors. In particular, we show explicitly how all symmetry-breaking features are encoded in the subleading eigenvectors of the degenerate subspace. Moreover, by partitioning configuration space into equivalence classes according to a proper order parameter, we achieve a substantial dimensional reduction which allows for the quantitative characterization of the spectral fingerprints of DPTs. We illustrate our predictions in several paradigmatic many-body systems, including (1) the one-dimensional boundary-driven weakly asymmetric exclusion process (WASEP), which exhibits a particle-hole symmetry-breaking DPT for current fluctuations, (2) the three- and four-state Potts model for spin dynamics, which displays discrete rotational symmetry-breaking DPTs for energy fluctuations, and (3) the closed WASEP which presents a continuous symmetry-breaking DPT into a time-crystal phase characterized by a rotating condensate.
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Affiliation(s)
- R Hurtado-Gutiérrez
- Institute Carlos I for Theoretical and Computational Physics, and Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, Granada 18071, Spain
| | - P I Hurtado
- Institute Carlos I for Theoretical and Computational Physics, and Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, Granada 18071, Spain
| | - C Pérez-Espigares
- Institute Carlos I for Theoretical and Computational Physics, and Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, Granada 18071, Spain
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9
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Mukherjee S, Smith NR. Dynamical phase transition in the occupation fraction statistics for noncrossing Brownian particles. Phys Rev E 2023; 107:064133. [PMID: 37464710 DOI: 10.1103/physreve.107.064133] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2023] [Accepted: 06/09/2023] [Indexed: 07/20/2023]
Abstract
We consider a system of N noncrossing Brownian particles in one dimension. We find the exact rate function that describes the long-time large deviation statistics of their occupation fraction in a finite interval in space. Remarkably, we find that, for any general N≥2, the system undergoes N-1 dynamical phase transitions of second order. The N-1 transitions are the boundaries of N phases that correspond to different numbers of particles which are in the vicinity of the interval throughout the dynamics. We achieve this by mapping the problem to that of finding the ground-state energy for N noninteracting spinless fermions in a square-well potential. The phases correspond to different numbers of single-body bound states for the quantum problem. We also study the process conditioned on a given occupation fraction and the large-N limiting behavior.
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Affiliation(s)
- Soheli Mukherjee
- Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus 8499000, Israel
| | - Naftali R Smith
- Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus 8499000, Israel
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10
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Devereux HL, Turner MS. Environmental Path-Entropy and Collective Motion. PHYSICAL REVIEW LETTERS 2023; 130:168201. [PMID: 37154632 DOI: 10.1103/physrevlett.130.168201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2022] [Revised: 01/18/2023] [Accepted: 03/28/2023] [Indexed: 05/10/2023]
Abstract
Inspired by the swarming or flocking of animal systems we study groups of agents moving in unbounded 2D space. Individual trajectories derive from a "bottom-up" principle: individuals reorient to maximize their future path entropy over environmental states. This can be seen as a proxy for keeping options open, a principle that may confer evolutionary fitness in an uncertain world. We find an ordered (coaligned) state naturally emerges, as well as disordered states or rotating clusters; similar phenotypes are observed in birds, insects, and fish, respectively. The ordered state exhibits an order-disorder transition under two forms of noise: (i) standard additive orientational noise, applied to the postdecision orientations and (ii) "cognitive" noise, overlaid onto each individual's model of the future paths of other agents. Unusually, the order increases at low noise, before later decreasing through the order-disorder transition as the noise increases further.
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Affiliation(s)
- Harvey L Devereux
- Department of Mathematics, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Matthew S Turner
- Department of Physics and Centre for Complexity Science, University of Warwick, Coventry CV4 7AL, United Kingdom and Department of Chemical Engineering, Kyoto University, Kyoto 615-8510, Japan
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11
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Omar AK, Klymko K, GrandPre T, Geissler PL, Brady JF. Tuning nonequilibrium phase transitions with inertia. J Chem Phys 2023; 158:074904. [PMID: 36813709 DOI: 10.1063/5.0138256] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023] Open
Abstract
In striking contrast to equilibrium systems, inertia can profoundly alter the structure of active systems. Here, we demonstrate that driven systems can exhibit effective equilibrium-like states with increasing particle inertia, despite rigorously violating the fluctuation-dissipation theorem. Increasing inertia progressively eliminates motility-induced phase separation and restores equilibrium crystallization for active Brownian spheres. This effect appears to be general for a wide class of active systems, including those driven by deterministic time-dependent external fields, whose nonequilibrium patterns ultimately disappear with increasing inertia. The path to this effective equilibrium limit can be complex, with finite inertia sometimes acting to accentuate nonequilibrium transitions. The restoration of near equilibrium statistics can be understood through the conversion of active momentum sources to passive-like stresses. Unlike truly equilibrium systems, the effective temperature is now density dependent, the only remnant of the nonequilibrium dynamics. This density-dependent temperature can in principle introduce departures from equilibrium expectations, particularly in response to strong gradients. Our results provide additional insight into the effective temperature ansatz while revealing a mechanism to tune nonequilibrium phase transitions.
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Affiliation(s)
- Ahmad K Omar
- Department of Materials Science and Engineering, University of California, Berkeley, California 94720, USA
| | - Katherine Klymko
- NERSC, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Trevor GrandPre
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Phillip L Geissler
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - John F Brady
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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12
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Garrahan JP, Manai C, Warzel S. Trajectory phase transitions in non-interacting systems: all-to-all dynamics and the random energy model. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20210415. [PMID: 36463921 DOI: 10.1098/rsta.2021.0415] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2022] [Accepted: 07/18/2022] [Indexed: 06/17/2023]
Abstract
We study the fluctuations of time-additive random observables in the stochastic dynamics of a system of [Formula: see text] non-interacting Ising spins. We mainly consider the case of all-to-all dynamics where transitions are possible between any two spin configurations with uniform rates. We show that the cumulant generating function of the time-integral of a normally distributed quenched random function of configurations, i.e. the energy function of the random energy model (REM), has a phase transition in the large [Formula: see text] limit for trajectories of any time extent. We prove this by determining the exact limit of the scaled cumulant generating function. This is accomplished by connecting the dynamical problem to a spectral analysis of the all-to-all quantum REM. We also discuss finite [Formula: see text] corrections as observed in numerical simulations. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.
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Affiliation(s)
- Juan P Garrahan
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, UK
| | - Chokri Manai
- Department of Mathematics, TU Munich, Germany
- MCQST, Munich, Germany
| | - Simone Warzel
- Department of Mathematics, TU Munich, Germany
- Department of Physics, TU Munich, Germany
- MCQST, Munich, Germany
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13
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Hecht L, Mandal S, Löwen H, Liebchen B. Active Refrigerators Powered by Inertia. PHYSICAL REVIEW LETTERS 2022; 129:178001. [PMID: 36332249 DOI: 10.1103/physrevlett.129.178001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2021] [Revised: 05/09/2022] [Accepted: 09/14/2022] [Indexed: 06/16/2023]
Abstract
We present the operational principle for a refrigerator that uses inertial effects in active Brownian particles to locally reduce their (kinetic) temperature by 2 orders of magnitude below the environmental temperature. This principle exploits the peculiar but so-far unknown shape of the phase diagram of inertial active Brownian particles to initiate motility-induced phase separation in the targeted cooling regime only. Remarkably, active refrigerators operate without requiring isolating walls opening the route toward using them to systematically absorb and trap, e.g., toxic substances from the environment.
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Affiliation(s)
- Lukas Hecht
- Institut für Physik kondensierter Materie, Technische Universität Darmstadt, Hochschulstraße 8, D-64289 Darmstadt, Germany
| | - Suvendu Mandal
- Institut für Physik kondensierter Materie, Technische Universität Darmstadt, Hochschulstraße 8, D-64289 Darmstadt, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II-Soft Matter, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
| | - Benno Liebchen
- Institut für Physik kondensierter Materie, Technische Universität Darmstadt, Hochschulstraße 8, D-64289 Darmstadt, Germany
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14
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Lamtyugina A, Qiu Y, Fodor É, Dinner AR, Vaikuntanathan S. Thermodynamic Control of Activity Patterns in Cytoskeletal Networks. PHYSICAL REVIEW LETTERS 2022; 129:128002. [PMID: 36179154 PMCID: PMC10014041 DOI: 10.1103/physrevlett.129.128002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2022] [Accepted: 07/26/2022] [Indexed: 06/16/2023]
Abstract
Biological materials, such as the actin cytoskeleton, exhibit remarkable structural adaptability to various external stimuli by consuming different amounts of energy. In this Letter, we use methods from large deviation theory to identify a thermodynamic control principle for structural transitions in a model cytoskeletal network. Specifically, we demonstrate that biasing the dynamics with respect to the work done by nonequilibrium components effectively renormalizes the interaction strength between such components, which can eventually result in a morphological transition. Our work demonstrates how a thermodynamic quantity can be used to renormalize effective interactions, which in turn can tune structure in a predictable manner, suggesting a thermodynamic principle for the control of cytoskeletal structure and dynamics.
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Affiliation(s)
| | - Yuqing Qiu
- Department of Chemistry, University of Chicago, Chicago, IL 60637
- James Franck Institute, University of Chicago, Chicago, IL 60637
| | - Étienne Fodor
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg
| | - Aaron R. Dinner
- Department of Chemistry, University of Chicago, Chicago, IL 60637
- James Franck Institute, University of Chicago, Chicago, IL 60637
| | - Suriyanarayanan Vaikuntanathan
- Department of Chemistry, University of Chicago, Chicago, IL 60637
- James Franck Institute, University of Chicago, Chicago, IL 60637
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15
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Horii H, Lefevere R, Itami M, Nemoto T. Anomalous fluctuations of renewal-reward processes with heavy-tailed distributions. Phys Rev E 2022; 106:034130. [PMID: 36266861 DOI: 10.1103/physreve.106.034130] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2022] [Accepted: 09/07/2022] [Indexed: 06/16/2023]
Abstract
For renewal-reward processes with a power-law decaying waiting time distribution, anomalously large probabilities are assigned to atypical values of the asymptotic processes. Previous works have revealed that this anomalous scaling causes a singularity in the corresponding large deviation function. In order to further understand this problem, we study in this article the scaling of variance in several renewal-reward processes: counting processes with two different power-law decaying waiting time distributions and a Knudsen gas (a heat conduction model). Through analytical and numerical analyses of these models, we find that the variances show an anomalous scaling when the exponent of the power law is -3. For a counting process with the power-law exponent smaller than -3, this anomalous scaling does not take place: this indicates that if we only consider the standard deviation from the expectation, any anomalous behavior will not be detected. In this case, we argue that anomalous scaling appears in higher order cumulants. Finally, many-body particles interacting through soft-core interactions with the boundary conditions employed in the Knudsen gas are studied using numerical simulations. We observe that the variance scaling becomes normal even though the power-law exponent in the boundary conditions is -3.
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Affiliation(s)
- Hiroshi Horii
- Université Paris Cité, Laboratoire de Probabilités, Statistiques et Modélisation, UMR 8001, F-75205 Paris, France
| | - Raphaël Lefevere
- Université Paris Cité, Laboratoire de Probabilités, Statistiques et Modélisation, UMR 8001, F-75205 Paris, France
| | - Masato Itami
- Center for Science Adventure and Collaborative Research Advancement, Kyoto University, Kyoto 606-8502, Japan
| | - Takahiro Nemoto
- Graduate School of Informatics, Kyoto University, Yoshida Hon-machi, Sakyo-ku, Kyoto 606-8501, Japan
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16
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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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17
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Rassolov G, Tociu L, Fodor E, Vaikuntanathan S. From predicting to learning dissipation from pair correlations of active liquids. J Chem Phys 2022; 157:054901. [DOI: 10.1063/5.0097863] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Active systems, which are driven out of equilibrium by local non-conservative forces, can adopt unique behaviors and configurations. Towards designing such materials, an important challenge is to precisely connect the static structure of active systems to the dissipation of energy induced by the local driving. Here, we use tools from liquid-state theories and machine learning to take on these challenges. We first demonstrate analytically for an isotropic active matter system that dissipation and pair correlations are closely related when driving forces behave like an active temperature. We then extend a nonequilibrium mean-field framework for predicting these pair correlations which, unlike most existing approaches, is applicable even for strongly interacting particles and far from equilibrium, to predict dissipation in these systems. Based on this theory, we reveal analytically a robust relation between dissipation and structure which holds even as the system approaches a nonequilibrium phase transition. Finally, we construct a neural network which maps static configurations of particles to their dissipation rate without any prior knowledge of the underlying dynamics. Our results open novel perspectives on the interplay between dissipation and organization out-of-equilibrium.
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Affiliation(s)
| | - Laura Tociu
- The University of Chicago, United States of America
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18
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Meibohm J, Esposito M. Finite-Time Dynamical Phase Transition in Nonequilibrium Relaxation. PHYSICAL REVIEW LETTERS 2022; 128:110603. [PMID: 35362998 DOI: 10.1103/physrevlett.128.110603] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2021] [Revised: 01/20/2022] [Accepted: 02/25/2022] [Indexed: 06/14/2023]
Abstract
We uncover a finite-time dynamical phase transition in the thermal relaxation of a mean-field magnetic model. The phase transition manifests itself as a cusp singularity in the probability distribution of the magnetization that forms at a critical time. The transition is due to a sudden switch in the dynamics, characterized by a dynamical order parameter. We derive a dynamical Landau theory for the transition that applies to a range of systems with scalar, parity-invariant order parameters. Close to criticalilty, our theory reveals an exact mapping between the dynamical and equilibrium phase transitions of the magnetic model, and implies critical exponents of mean-field type. We argue that interactions between nearby saddle points, neglected at the mean-field level, may lead to critical, spatiotemporal fluctuations of the order parameter, and thus give rise to novel, dynamical critical phenomena.
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Affiliation(s)
- Jan Meibohm
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
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19
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Das A, Kuznets-Speck B, Limmer DT. Direct Evaluation of Rare Events in Active Matter from Variational Path Sampling. PHYSICAL REVIEW LETTERS 2022; 128:028005. [PMID: 35089729 DOI: 10.1103/physrevlett.128.028005] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2021] [Accepted: 12/09/2021] [Indexed: 06/14/2023]
Abstract
Active matter represents a broad class of systems that evolve far from equilibrium due to the local injection of energy. Like their passive analogs, transformations between distinct metastable states in active matter proceed through rare fluctuations; however, their detailed balance violating dynamics renders these events difficult to study. Here, we present a simulation method for evaluating the rate and mechanism of rare events in generic nonequilibrium systems and apply it to study the conformational changes of a passive solute in an active fluid. The method employs a variational optimization of a control force that renders the rare event a typical one, supplying an exact estimate of its rate as a ratio of path partition functions. Using this method we find that increasing activity in the active bath can enhance the rate of conformational switching of the passive solute in a manner consistent with recent bounds from stochastic thermodynamics.
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Affiliation(s)
- Avishek Das
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | | | - David T Limmer
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawerence Berkeley National Laboratory, Berkeley, California 94720, USA
- Material Sciences Division, Lawerence Berkeley National Laboratory, Berkeley, California 94720, USA
- Kavli Energy NanoSciences Institute, University of California, Berkeley, California 94720, USA
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20
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Cao Z, Jiang H, Hou Z. Designing circle swimmers: Principles and strategies. J Chem Phys 2021; 155:234901. [PMID: 34937364 DOI: 10.1063/5.0065529] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Various microswimmers move along circles rather than straight lines due to their swimming mechanisms, body shapes, or hydrodynamic effects. In this paper, we adopt the concepts of stochastic thermodynamics to analyze circle swimmers confined to a two-dimensional plane and study the trade-off relations between various physical quantities, such as precision, energy cost, and rotational speed. Based on these findings, we predict principles and strategies for designing microswimmers of special optimized functions under limited energy resource conditions, which will bring new experimental inspiration for designing smart motors.
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Affiliation(s)
- Zhiyu Cao
- Department of Chemical Physics and Hefei National Laboratory for Physical Sciences at Microscales, iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Huijun Jiang
- Department of Chemical Physics and 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 and Hefei National Laboratory for Physical Sciences at Microscales, iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China
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21
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Gutiérrez CMB, Vanhille-Campos C, Alarcón F, Pagonabarraga I, Brito R, Valeriani C. Collective motion of run-and-tumble repulsive and attractive particles in one-dimensional systems. SOFT MATTER 2021; 17:10479-10491. [PMID: 34750600 DOI: 10.1039/d1sm01006a] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Active matter deals with systems whose particles consume energy at the individual level in order to move. To unravel features such as the emergence of collective structures, several models have been suggested, such as the on-lattice model of run-and-tumble particles implemented via the persistent exclusion process (PEP). In our work, we study a one-dimensional system of run-and-tumble repulsive or attractive particles, both on-lattice and off-lattice. Additionally, we implement cluster motility dynamics in the on-lattice case (since in the off-lattice case, cluster motility arises from the individual particle dynamics). While we observe important differences between discrete and continuous dynamics, few common features are of particular importance. Increasing particle density drives aggregation across all different systems explored. For non-attractive particles, the effects of particle activity on aggregation are largely independent of the details of the dynamics. In contrast, once attractive interactions are introduced, the steady-state, which is completely determined by the interplay between these and the particles' activity, becomes highly dependent on the details of the dynamics.
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Affiliation(s)
- C Miguel Barriuso Gutiérrez
- Departamento de Estructura de la Materia, Física Térmica y Electrónica, Facultad de Ciencias Físicas, Universidad Complutense de Madrid, 28040, Madrid, Spain.
| | - Christian Vanhille-Campos
- Departamento de Estructura de la Materia, Física Térmica y Electrónica, Facultad de Ciencias Físicas, Universidad Complutense de Madrid, 28040, Madrid, Spain.
- Department of Physics and Astronomy, University College London, London WC1E 6BT, UK
- Institute for the Physics of Living Systems, University College London, London WC1E 6BT, UK
- MRC Laboratory for Molecular Cell Biology, University College London, London WC1E 6BT, UK
| | - Francisco Alarcón
- Departamento de Estructura de la Materia, Física Térmica y Electrónica, Facultad de Ciencias Físicas, Universidad Complutense de Madrid, 28040, Madrid, Spain.
- Departamento de Ingeniería Física, División de Ciencias e Ingenierías, Universidad de Guanajuato, Loma del Bosque 103, 37150 León, Mexico
| | - Ignacio Pagonabarraga
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, 08028 Barcelona, Spain
- Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, 08028 Barcelona, Spain
- CECAM, Centre Européen de Calcul Atomique et Moléculaire, École Polytechnique Fédérale de Lasuanne (EPFL), Batochime, Avenue Forel 2, 1015 Lausanne, Switzerland
| | - Ricardo Brito
- Departamento de Estructura de la Materia, Física Térmica y Electrónica, Facultad de Ciencias Físicas, Universidad Complutense de Madrid, 28040, Madrid, Spain.
- GISC - Grupo Interdisciplinar de Sistemas Complejos, 28040, Madrid, Spain
| | - Chantal Valeriani
- Departamento de Estructura de la Materia, Física Térmica y Electrónica, Facultad de Ciencias Físicas, Universidad Complutense de Madrid, 28040, Madrid, Spain.
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22
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Das A, Rose DC, Garrahan JP, Limmer DT. Reinforcement learning of rare diffusive dynamics. J Chem Phys 2021; 155:134105. [PMID: 34624994 DOI: 10.1063/5.0057323] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a method to probe rare molecular dynamics trajectories directly using reinforcement learning. We consider trajectories that are conditioned to transition between regions of configuration space in finite time, such as those relevant in the study of reactive events, and trajectories exhibiting rare fluctuations of time-integrated quantities in the long time limit, such as those relevant in the calculation of large deviation functions. In both cases, reinforcement learning techniques are used to optimize an added force that minimizes the Kullback-Leibler divergence between the conditioned trajectory ensemble and a driven one. Under the optimized added force, the system evolves the rare fluctuation as a typical one, affording a variational estimate of its likelihood in the original trajectory ensemble. Low variance gradients employing value functions are proposed to increase the convergence of the optimal force. The method we develop employing these gradients leads to efficient and accurate estimates of both the optimal force and the likelihood of the rare event for a variety of model systems.
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Affiliation(s)
- Avishek Das
- Department of Chemistry, University of California, Berkeley, California 94609, USA
| | - Dominic C Rose
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Juan P Garrahan
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - David T Limmer
- Department of Chemistry, University of California, Berkeley, California 94609, USA
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23
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24
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Dissipation bounds the amplification of transition rates far from equilibrium. Proc Natl Acad Sci U S A 2021; 118:2020863118. [PMID: 33593915 DOI: 10.1073/pnas.2020863118] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
Abstract
Complex systems can convert energy imparted by nonequilibrium forces to regulate how quickly they transition between long-lived states. While such behavior is ubiquitous in natural and synthetic systems, currently there is no general framework to relate the enhancement of a transition rate to the energy dissipated or to bound the enhancement achievable for a given energy expenditure. We employ recent advances in stochastic thermodynamics to build such a framework, which can be used to gain mechanistic insight into transitions far from equilibrium. We show that under general conditions, there is a basic speed limit relating the typical excess heat dissipated throughout a transition and the rate amplification achievable. We illustrate this tradeoff in canonical examples of diffusive barrier crossings in systems driven with autonomous and deterministic external forcing protocols. In both cases, we find that our speed limit tightly constrains the rate enhancement.
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25
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Dolezal J, Jack RL. Long-ranged correlations in large deviations of local clustering. Phys Rev E 2021; 103:052132. [PMID: 34134232 DOI: 10.1103/physreve.103.052132] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2020] [Accepted: 04/19/2021] [Indexed: 11/07/2022]
Abstract
In systems of diffusing particles, we investigate large deviations of a time-averaged measure of clustering around one particle. We focus on biased ensembles of trajectories, which realize large-deviation events. The bias acts on a single particle, but elicits a response that spans the whole system. We analyze this effect through the lens of macroscopic fluctuation theory, focusing on the coupling of the bias to hydrodynamic modes. This explains that the dynamical free energy has nontrivial scaling relationships with the system size, in 1 and 2 spatial dimensions. We show that the long-ranged response to a bias on one particle also has consequences when biasing two particles.
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Affiliation(s)
- Jakub Dolezal
- DAMTP, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Robert L Jack
- DAMTP, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.,Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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26
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Omar AK, Klymko K, GrandPre T, Geissler PL. Phase Diagram of Active Brownian Spheres: Crystallization and the Metastability of Motility-Induced Phase Separation. PHYSICAL REVIEW LETTERS 2021; 126:188002. [PMID: 34018789 DOI: 10.1103/physrevlett.126.188002] [Citation(s) in RCA: 30] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2020] [Revised: 03/06/2021] [Accepted: 04/05/2021] [Indexed: 06/12/2023]
Abstract
Motility-induced phase separation (MIPS), the phenomenon in which purely repulsive active particles undergo a liquid-gas phase separation, is among the simplest and most widely studied examples of a nonequilibrium phase transition. Here, we show that states of MIPS coexistence are in fact only metastable for three-dimensional active Brownian particles over a very broad range of conditions, decaying at long times through an ordering transition we call active crystallization. At an activity just above the MIPS critical point, the liquid-gas binodal is superseded by the crystal-fluid coexistence curve, with solid, liquid, and gas all coexisting at the triple point where the two curves intersect. Nucleating an active crystal from a disordered fluid, however, requires a rare fluctuation that exhibits the nearly close-packed density of the solid phase. The corresponding barrier to crystallization is surmountable on a feasible timescale only at high activity, and only at fluid densities near maximal packing. The glassiness expected for such dense liquids at equilibrium is strongly mitigated by active forces, so that the lifetime of liquid-gas coexistence declines steadily with increasing activity, manifesting in simulations as a facile spontaneous crystallization at extremely high activity.
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Affiliation(s)
- Ahmad K Omar
- Department of Materials Science and Engineering, University of California, Berkeley, California 94720, USA
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Katherine Klymko
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- NERSC, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Trevor GrandPre
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Phillip L Geissler
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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27
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Whitelam S, Jacobson D. Varied phenomenology of models displaying dynamical large-deviation singularities. Phys Rev E 2021; 103:032152. [PMID: 33862814 DOI: 10.1103/physreve.103.032152] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2021] [Accepted: 03/16/2021] [Indexed: 11/07/2022]
Abstract
Singularities of dynamical large-deviation functions are often interpreted as the signal of a dynamical phase transition and the coexistence of distinct dynamical phases, by analogy with the correspondence between singularities of free energies and equilibrium phase behavior. Here we study models of driven random walkers on a lattice. These models display large-deviation singularities in the limit of large lattice size, but the extent to which each model's phenomenology resembles a phase transition depends on the details of the driving. We also compare the behavior of ergodic and nonergodic models that present large-deviation singularities. We argue that dynamical large-deviation singularities indicate the divergence of a model timescale, but not necessarily one associated with cooperative behavior or the existence of distinct phases.
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Affiliation(s)
- Stephen Whitelam
- Molecular Foundry, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA
| | - Daniel Jacobson
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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28
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Martin D, O'Byrne J, Cates ME, Fodor É, Nardini C, Tailleur J, van Wijland F. Statistical mechanics of active Ornstein-Uhlenbeck particles. Phys Rev E 2021; 103:032607. [PMID: 33862678 DOI: 10.1103/physreve.103.032607] [Citation(s) in RCA: 61] [Impact Index Per Article: 20.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2020] [Accepted: 12/23/2020] [Indexed: 06/12/2023]
Abstract
We study the statistical properties of active Ornstein-Uhlenbeck particles (AOUPs). In this simplest of models, the Gaussian white noise of overdamped Brownian colloids is replaced by a Gaussian colored noise. This suffices to grant this system the hallmark properties of active matter, while still allowing for analytical progress. We study in detail the steady-state distribution of AOUPs in the small persistence time limit and for spatially varying activity. At the collective level, we show AOUPs to experience motility-induced phase separation both in the presence of pairwise forces or due to quorum-sensing interactions. We characterize both the instability mechanism leading to phase separation and the resulting phase coexistence. We probe how, in the stationary state, AOUPs depart from their thermal equilibrium limit by investigating the emergence of ratchet currents and entropy production. In the small persistence time limit, we show how fluctuation-dissipation relations are recovered. Finally, we discuss how the emerging properties of AOUPs can be characterized from the dynamics of their collective modes.
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Affiliation(s)
- David Martin
- Université de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS,F-75205 Paris, France
| | - Jérémy O'Byrne
- Université de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS,F-75205 Paris, France
| | - Michael E Cates
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Étienne Fodor
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg
| | - Cesare Nardini
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- Service de Physique de l'État Condensé, CNRS UMR 3680, CEA-Saclay, 91191 Gif-sur-Yvette, France
| | - Julien Tailleur
- Université de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS,F-75205 Paris, France
| | - Frédéric van Wijland
- Université de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS,F-75205 Paris, France
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29
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GrandPre T, Klymko K, Mandadapu KK, Limmer DT. Entropy production fluctuations encode collective behavior in active matter. Phys Rev E 2021; 103:012613. [PMID: 33601608 DOI: 10.1103/physreve.103.012613] [Citation(s) in RCA: 22] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2020] [Accepted: 12/22/2020] [Indexed: 11/07/2022]
Abstract
We derive a general lower bound on distributions of entropy production in interacting active matter systems. The bound is tight in the limit that interparticle correlations are small and short-ranged, which we explore in four canonical active matter models. In all models studied, the bound is weak where collective fluctuations result in long-ranged correlations, which subsequently links the locations of phase transitions to enhanced entropy production fluctuations. We develop a theory for the onset of enhanced fluctuations and relate it to specific phase transitions in active Brownian particles. We also derive optimal control forces that realize the dynamics necessary to tune dissipation and manipulate the system between phases. In so doing, we uncover a general relationship between entropy production and pattern formation in active matter, as well as ways of controlling it.
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Affiliation(s)
- Trevor GrandPre
- Department of Physics, University of California, Berkeley, California 94609, USA
| | - Katherine Klymko
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94609, USA
| | - Kranthi K Mandadapu
- Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94609, USA.,Chemical Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94609, USA
| | - David T Limmer
- Chemical Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94609, USA.,Department of Chemistry, University of California, Berkeley, California 94609, USA.,Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94609, USA.,Kavli Energy NanoScience Institute, Berkeley, California 94609, USA
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30
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Keta YE, Fodor É, van Wijland F, Cates ME, Jack RL. Collective motion in large deviations of active particles. Phys Rev E 2021; 103:022603. [PMID: 33736055 DOI: 10.1103/physreve.103.022603] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2020] [Accepted: 01/12/2021] [Indexed: 06/12/2023]
Abstract
We analyze collective motion that occurs during rare (large deviation) events in systems of active particles, both numerically and analytically. We discuss the associated dynamical phase transition to collective motion, which occurs when the active work is biased towards larger values, and is associated with alignment of particles' orientations. A finite biasing field is needed to induce spontaneous symmetry breaking, even in large systems. Particle alignment is computed exactly for a system of two particles. For many-particle systems, we analyze the symmetry breaking by an optimal-control representation of the biased dynamics, and we propose a fluctuating hydrodynamic theory that captures the emergence of polar order in the biased state.
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Affiliation(s)
- Yann-Edwin Keta
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- Université de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France
- Département de Physique, École normale supérieure de Lyon, 69364 Lyon Cedex 07, France
| | - Étienne Fodor
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg
| | - Frédéric van Wijland
- Université de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France
| | - Michael E Cates
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Robert L Jack
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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31
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Turci F, Wilding NB. Phase Separation and Multibody Effects in Three-Dimensional Active Brownian Particles. PHYSICAL REVIEW LETTERS 2021; 126:038002. [PMID: 33543975 DOI: 10.1103/physrevlett.126.038002] [Citation(s) in RCA: 22] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2020] [Accepted: 12/14/2020] [Indexed: 06/12/2023]
Abstract
Simulation studies of the phase diagram of repulsive active Brownian particles in three dimensions reveal that the region of motility-induced phase separation between a high and low density phase is enclosed by a region of gas-crystal phase separation. Near-critical loci and structural crossovers can additionally be identified in analogy with simple fluids. Motivated by the striking similarity to the behavior of equilibrium fluids with short-ranged pairwise attractions, we show that a direct mapping to pair potentials in the dilute limit implies interactions that are insufficiently attractive to engender phase separation. Instead, this is driven by the emergence of multibody effects associated with particle caging that occurs at sufficiently high number density. We quantify these effects via information-theoretical measures of n-body effective interactions extracted from the configurational structure.
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Affiliation(s)
- Francesco Turci
- H. H. Wills Physics Laboratory, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom
| | - Nigel B Wilding
- H. H. Wills Physics Laboratory, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom
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32
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Zarif M, Naji A. Confinement-induced alternating interactions between inclusions in an active fluid. Phys Rev E 2020; 102:032613. [PMID: 33075886 DOI: 10.1103/physreve.102.032613] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2019] [Accepted: 09/08/2020] [Indexed: 11/07/2022]
Abstract
In a system of colloidal inclusions suspended in an equilibrium bath of smaller particles, the particulate bath engenders effective, short-ranged, primarily attractive interactions between the inclusions, known as depletion interactions, that originate from the steric depletion of bath particles from the immediate vicinity of the inclusions. In a bath of active (self-propelled) particles, the nature of such bath-mediated interactions can qualitatively change from attraction to repulsion, and they become stronger in magnitude and range of action as compared with typical equilibrium depletion interactions, especially as the bath activity (particle self-propulsion) is increased. We study effective interactions mediated by a bath of active Brownian particles between two fixed, impenetrable, and disk-shaped inclusions in a planar (channel) confinement in two dimensions. Confinement is found to strongly influence the effective interaction between the inclusions, specifically by producing alternating interaction profiles with possible attractive and repulsive regions in sufficiently narrow channels. We study the dependence of the ensuing interactions on different system parameters and the orientational (parallel versus perpendicular) configuration of the inclusion pair relative to the channel walls. The confinement effects are largely regulated by the layering of active particles next to the surface boundaries, both of the inclusions and the channel walls that counteract one another in accumulating the active particles in their own proximities. In narrow channels, the combined effects due to the channel walls and the inclusions lead to peculiar structuring of active particles (reminiscent of wavelike interference patterns) within the channel.
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Affiliation(s)
- Mahdi Zarif
- Department of Physical and Computational Chemistry, Shahid Beheshti University, Tehran 19839-9411, Iran
| | - Ali Naji
- School of Physics, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5531, Iran.,School of Nano Science, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5531, Iran
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33
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Das S, Ghosh S, Chelakkot R. Aggregate morphology of active Brownian particles on porous, circular walls. Phys Rev E 2020; 102:032619. [PMID: 33075888 DOI: 10.1103/physreve.102.032619] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2020] [Accepted: 09/10/2020] [Indexed: 06/11/2023]
Abstract
We study the motility-induced aggregation of active Brownian particles (ABPs) on a porous, circular wall. We observe that the morphology of aggregated dense-phase on a static wall depends on the wall porosity, particle motility, and the radius of the circular wall. Our analysis reveals two morphologically distinct, dense aggregates; a connected dense cluster that spreads uniformly on the circular wall and a localized cluster that breaks the rotational symmetry of the system. These distinct morphological states are similar to the macroscopic structures observed in aggregates on planar, porous walls. We systematically analyze the parameter regimes where the different morphological states are observed. We further extend our analysis to motile circular rings. We show that the motile ring propels almost ballistically due to the force applied by the active particles when they form a localized cluster, whereas it moves diffusively when the active particles form a continuous cluster. This property demonstrates the possibility of extracting useful work from a system of ABPs, even without artificially breaking the rotational symmetry.
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Affiliation(s)
- Suchismita Das
- Department of Physics, Indian Institute of Technology Bombay, Mumbai 400076, India
| | - Sounok Ghosh
- Department of Physics, Indian Institute of Technology Bombay, Mumbai 400076, India
| | - Raghunath Chelakkot
- Department of Physics, Indian Institute of Technology Bombay, Mumbai 400076, India
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34
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Ekeh T, Cates ME, Fodor É. Thermodynamic cycles with active matter. Phys Rev E 2020; 102:010101. [PMID: 32795058 DOI: 10.1103/physreve.102.010101] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2020] [Accepted: 06/03/2020] [Indexed: 11/07/2022]
Abstract
Active matter constantly dissipates energy to power the self-propulsion of its microscopic constituents. This opens the door to designing innovative cyclic engines without any equilibrium equivalent. We offer a consistent thermodynamic framework to characterize and optimize the performances of such cycles. Based on a minimal model, we put forward a protocol which extracts work by controlling only the properties of the confining walls at boundaries, and we rationalize the transitions between optimal cycles. We show that the corresponding power and efficiency are generally proportional, so that they reach their maximum values at the same cycle time in contrast with thermal cycles, and we provide a generic relation constraining the fluctuations of the power.
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Affiliation(s)
- Timothy Ekeh
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Michael E Cates
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Étienne Fodor
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
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35
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Cagnetta F, Mallmin E. Efficiency of one-dimensional active transport conditioned on motility. Phys Rev E 2020; 101:022130. [PMID: 32168590 DOI: 10.1103/physreve.101.022130] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2019] [Accepted: 02/06/2020] [Indexed: 12/22/2022]
Abstract
By conditioning a stochastic process on the value of an observable, one obtains a new stochastic process with different properties. We apply this idea in the context of active matter and condition interacting self-propelled particles on their individual motility. Using the effective process formalism from dynamical large deviations theory, we derive the interactions that actuate the imposed mobility against jamming interactions in two toy models-the totally asymmetric exclusion process and run-and-tumble particles, in the case of two or three particles. We provide a framework which takes into account the energy-consumption required for self-propulsion and address the question of how energy-efficient the emergent interactions are. Upon conditioning, run-and-tumble particles develop an alignment interaction and achieve a higher gain in efficiency than TASEP particles. A point of diminishing returns in efficiency is reached beyond a certain level of conditioning. With recourse to a general formula for the change in energy efficiency upon conditioning, we conclude that the most significant gains occur when there are large fluctuations in mobility to exploit. From a detailed comparison of the emergent effective interaction in a two- versus a three-body scenario, we discover evidence of a screening effect which suggests that conditioning can produce topological rather than metric interactions.
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Affiliation(s)
- F Cagnetta
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - E Mallmin
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
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36
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Crosato E, Prokopenko M, Spinney RE. Irreversibility and emergent structure in active matter. Phys Rev E 2019; 100:042613. [PMID: 31770893 DOI: 10.1103/physreve.100.042613] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2019] [Indexed: 06/10/2023]
Abstract
Active matter is rapidly becoming a key paradigm of out-of-equilibrium soft matter exhibiting complex collective phenomena, yet the thermodynamics of such systems remain poorly understood. In this article we study the dynamical irreversibility of large-scale active systems capable of motility-induced phase separation and polar alignment. We use a model with momenta in both translational and rotational degrees of freedom, revealing a hidden component not previously reported in the literature. Steady-state irreversibility is quantified at each point in the phase diagram which exhibits sharp discontinuities at phase transitions. Identification of the irreversibility in individual particles lays the groundwork for discussion of the thermodynamics of microfeatures, such as defects in the emergent structure. The interpretation of the time reversal symmetry in the dynamics of the particles is found to be crucial.
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Affiliation(s)
- Emanuele Crosato
- Complex Systems Research Group and Centre for Complex Systems, Faculty of Engineering, The University of Sydney, Sydney NSW 2006, Australia
- CSIRO Data61, P.O. Box 76, Epping NSW 1710, Australia
| | - Mikhail Prokopenko
- Complex Systems Research Group and Centre for Complex Systems, Faculty of Engineering, The University of Sydney, Sydney NSW 2006, Australia
| | - Richard E Spinney
- Complex Systems Research Group and Centre for Complex Systems, Faculty of Engineering, The University of Sydney, Sydney NSW 2006, Australia
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37
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García-García R, Collet P, Truskinovsky L. Guided active particles. Phys Rev E 2019; 100:042608. [PMID: 31771015 DOI: 10.1103/physreve.100.042608] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2018] [Indexed: 06/10/2023]
Abstract
To account for the possibility of an externally driven taxis in active systems, we develop a model of a guided active drift which relies on the presence of an external guiding field and a vectorial coupling between the mechanical degrees of freedom and a chemical reaction. To characterize the ability of guided active particles to carry cargo, we generalize the notion of Stokes efficiency extending it to the case of stall conditions. To show the generality of the proposed mechanism, we discuss guided electric circuits capable of turning fluctuations into a directed current without a source of voltage.
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Affiliation(s)
- Reinaldo García-García
- PMMH, CNRS UMR 7636, ESPCI Paris, Université PSL, 10 rue de Vauquelin, F-75005 Paris, France
| | - Pierre Collet
- CPHT, CNRS, École Polytechnique, Institut Polytechnique de Paris, F-91128 Palaiseau, France
| | - Lev Truskinovsky
- PMMH, CNRS UMR 7636, ESPCI Paris, Université PSL, 10 rue de Vauquelin, F-75005 Paris, France
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38
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Jack RL. Large deviations in models of growing clusters with symmetry-breaking transitions. Phys Rev E 2019; 100:012140. [PMID: 31499766 DOI: 10.1103/physreve.100.012140] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2019] [Indexed: 06/10/2023]
Abstract
We analyze large deviations of the magnetization in two models of growing clusters. The models have symmetry-breaking transitions, so the typical magnetization of a growing cluster may be either positive or negative, with equal probability. For large clusters, the magnetization obeys a large-deviation principle. We show that the corresponding rate function is zero for values of the magnetization that are intermediate between the two steady state values, which means that fluctuations with these values of the magnetization are much less unlikely than previously thought. We show that their probabilities decay as power laws in the cluster size, instead of the exponential scaling that would be expected from the large-deviation principle. We discuss how this observation is related to dynamical phase coexistence phenomena. We also comment on the typical size of magnetization fluctuations.
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Affiliation(s)
- Robert L Jack
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom and Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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Carenza LN, Gonnella G, Lamura A, Negro G, Tiribocchi A. Lattice Boltzmann methods and active fluids. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2019; 42:81. [PMID: 31250142 DOI: 10.1140/epje/i2019-11843-6] [Citation(s) in RCA: 34] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2019] [Accepted: 05/24/2019] [Indexed: 05/24/2023]
Abstract
We review the state of the art of active fluids with particular attention to hydrodynamic continuous models and to the use of Lattice Boltzmann Methods (LBM) in this field. We present the thermodynamics of active fluids, in terms of liquid crystals modelling adapted to describe large-scale organization of active systems, as well as other effective phenomenological models. We discuss how LBM can be implemented to solve the hydrodynamics of active matter, starting from the case of a simple fluid, for which we explicitly recover the continuous equations by means of Chapman-Enskog expansion. Going beyond this simple case, we summarize how LBM can be used to treat complex and active fluids. We then review recent developments concerning some relevant topics in active matter that have been studied by means of LBM: spontaneous flow, self-propelled droplets, active emulsions, rheology, active turbulence, and active colloids.
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Affiliation(s)
- Livio Nicola Carenza
- Dipartimento di Fisica, Università degli Studi di Bari, and INFN Sezione di Bari, Via Amendola 173, 70126, Bari, Italy
| | - Giuseppe Gonnella
- Dipartimento di Fisica, Università degli Studi di Bari, and INFN Sezione di Bari, Via Amendola 173, 70126, Bari, Italy.
| | - Antonio Lamura
- Istituto Applicazioni Calcolo, CNR, Via Amendola 122/D, 70126, Bari, Italy
| | - Giuseppe Negro
- Dipartimento di Fisica, Università degli Studi di Bari, and INFN Sezione di Bari, Via Amendola 173, 70126, Bari, Italy
| | - Adriano Tiribocchi
- Center for Life Nano Science@La Sapienza, Istituto Italiano di Tecnologia, 00161, Roma, Italy
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