1
|
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.
Collapse
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
| |
Collapse
|
2
|
Paoluzzi M, Puglisi A, Angelani L. Entropy Production of Run-and-Tumble Particles. ENTROPY (BASEL, SWITZERLAND) 2024; 26:443. [PMID: 38920452 PMCID: PMC11203161 DOI: 10.3390/e26060443] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2024] [Revised: 05/21/2024] [Accepted: 05/22/2024] [Indexed: 06/27/2024]
Abstract
We analyze the entropy production in run-and-tumble models. After presenting the general formalism in the framework of the Fokker-Planck equations in one space dimension, we derive some known exact results in simple physical situations (free run-and-tumble particles and harmonic confinement). We then extend the calculation to the case of anisotropic motion (different speeds and tumbling rates for right- and left-oriented particles), obtaining exact expressions of the entropy production rate. We conclude by discussing the general case of heterogeneous run-and-tumble motion described by space-dependent parameters and extending the analysis to the case of d-dimensional motions.
Collapse
Affiliation(s)
- Matteo Paoluzzi
- Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche, Via Pietro Castellino 111, I-80131 Napoli, Italy;
| | - Andrea Puglisi
- Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, Piazzale A. Moro 2, I-00185 Roma, Italy;
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale A. Moro 2, I-00185 Roma, Italy
| | - Luca Angelani
- Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, Piazzale A. Moro 2, I-00185 Roma, Italy;
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale A. Moro 2, I-00185 Roma, Italy
| |
Collapse
|
3
|
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.
Collapse
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
| |
Collapse
|
4
|
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.
Collapse
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
| |
Collapse
|
5
|
Dutta S. Most probable paths for active Ornstein-Uhlenbeck particles. Phys Rev E 2023; 107:054130. [PMID: 37329007 DOI: 10.1103/physreve.107.054130] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2022] [Accepted: 05/05/2023] [Indexed: 06/18/2023]
Abstract
Fluctuations play an important role in the dynamics of stochastic systems. In particular, for small systems, the most probable thermodynamic quantities differ from their averages because of the fluctuations. Using the Onsager Machlup variational formalism we analyze the most probable paths for nonequilibrium systems, in particular, active Ornstein-Uhlenbeck particles, and investigate how the entropy production along these paths differs from the average entropy production. We investigate how much information about their nonequilibrium nature can be obtained from their extremum paths and how these paths depend on the persistence time and their swim velocities. We also look at how the entropy production along the most probable paths varies with the active noise and how it differs from the average entropy production. This study would be useful to design artificial active systems with certain target trajectories.
Collapse
Affiliation(s)
- Sandipan Dutta
- Department of Physics, Birla Institute of Technology and Science, Pilani, Rajasthan, 333031, India
| |
Collapse
|
6
|
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.
Collapse
Affiliation(s)
- Derek Frydel
- Department of Chemistry, Universidad Técnica Federico Santa María, Campus San Joaquin, 7820275 Santiago, Chile
| |
Collapse
|
7
|
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.
Collapse
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
| |
Collapse
|
8
|
Lee JS, Park H. Effects of the non-Markovianity and non-Gaussianity of active environmental noises on engine performance. Phys Rev E 2022; 105:024130. [PMID: 35291119 DOI: 10.1103/physreve.105.024130] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2021] [Accepted: 02/11/2022] [Indexed: 06/14/2023]
Abstract
An active environment is a reservoir containing active materials, such as bacteria and Janus particles. Given the self-propelled motion of these materials, powered by chemical energy, an active environment has unique, nonequilibrium environmental noise. Recently, studies on engines that harvest energy from active environments have attracted a great deal of attention because the theoretical and experimental findings indicate that these engines outperform conventional ones. Studies have explored the features of active environments essential for outperformance, such as the non-Gaussian or non-Markovian nature of the active noise. We systematically study the effects of the non-Gaussianity and non-Markovianity of active noise on engine performance. We show that non-Gaussianity is irrelevant to the performance of an engine driven by any linear force (including a harmonic trap) regardless of time dependency, whereas non-Markovianity is relevant. However, for a system driven by a general nonlinear force, both non-Gaussianity and non-Markovianity enhance engine performance. Also, the memory effect of an active reservoir should be considered when fabricating a cyclic engine.
Collapse
Affiliation(s)
- Jae Sung Lee
- School of Physics and Quantum Universe Center, Korea Institute for Advanced Study, Seoul 02455, Korea
| | - Hyunggyu Park
- School of Physics and Quantum Universe Center, Korea Institute for Advanced Study, Seoul 02455, Korea
| |
Collapse
|
9
|
Vachier J, Wettlaufer JS. Premelting controlled active matter in ice. Phys Rev E 2022; 105:024601. [PMID: 35291135 DOI: 10.1103/physreve.105.024601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2021] [Accepted: 01/14/2022] [Indexed: 06/14/2023]
Abstract
Self-propelled particles can undergo complex dynamics due to a range of bulk and surface interactions. When a particle is embedded in a host solid near its bulk melting temperature, the latter may melt at the surface of the former in a process known as interfacial premelting. The thickness of the melt film depends on the temperature, impurities, material properties and geometry. A temperature gradient is accompanied by a thermomolecular pressure gradient that drives the interfacial liquid from high to low temperatures and hence the particle from low to high temperatures, in a process called thermal regelation. When the host material is ice and the embedded particle is a biological entity, one has a particularly different form of active matter, which addresses interplay between a wide range of problems, from extremophiles of both terrestrial and exobiological relevance to ecological dynamics in Earth's cryosphere. Of basic importance in all such settings is the combined influence of biological activity and thermal regelation in controlling the redistribution of bioparticles. Therefore, we recast this class of regelation phenomena in the stochastic framework of active Ornstein-Uhlenbeck dynamics and make predictions relevant to this and related problems of interest in biological and geophysical problems. We examine how thermal regelation compromises paleoclimate studies in the context of ice core dating and we find that the activity influences particle dynamics during thermal regelation by enhancing the effective diffusion coefficient. Therefore, accurate dating relies on a quantitative treatment of both effects.
Collapse
Affiliation(s)
- Jérémy Vachier
- Nordita, KTH Royal Institute of Technology and Stockholm University, Hannes Alfvéns väg 12, SE-106 91 Stockholm, Sweden
| | - J S Wettlaufer
- Nordita, KTH Royal Institute of Technology and Stockholm University, Hannes Alfvéns väg 12, SE-106 91 Stockholm, Sweden
- Yale University, New Haven, Connecticut 06520-8109, USA
| |
Collapse
|
10
|
Caprini L, Cecconi F, Marini Bettolo Marconi U. Correlated escape of active particles across a potential barrier. J Chem Phys 2021; 155:234902. [PMID: 34937362 DOI: 10.1063/5.0074072] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We study the dynamics of one-dimensional active particles confined in a double-well potential, focusing on the escape properties of the system, such as the mean escape time from a well. We first consider a single-particle both in near and far-from-equilibrium regimes by varying the persistence time of the active force and the swim velocity. A non-monotonic behavior of the mean escape time is observed with the persistence time of the activity, revealing the existence of an optimal choice of the parameters favoring the escape process. For small persistence times, a Kramers-like formula with an effective potential obtained within the unified colored noise approximation is shown to hold. Instead, for large persistence times, we developed a simple theoretical argument based on the first passage theory, which explains the linear dependence of the escape time with the persistence of the active force. In the second part of the work, we consider the escape on two active particles mutually repelling. Interestingly, the subtle interplay of active and repulsive forces may lead to a correlation between particles, favoring the simultaneous jump across the barrier. This mechanism cannot be observed in the escape process of two passive particles. Finally, we find that in the small persistence regime, the repulsion favors the escape, such as in passive systems, in agreement with our theoretical predictions, while for large persistence times, the repulsive and active forces produce an effective attraction, which hinders the barrier crossing.
Collapse
Affiliation(s)
- Lorenzo Caprini
- Heinrich-Heine-University of Düsseldorf, Universitätsstrasse 1, Düsseldorf, Germany
| | - Fabio Cecconi
- Scuola di Scienze e Tecnologie, Università di Camerino, Via Madonna delle Carceri, I-62032 Camerino, Italy
| | | |
Collapse
|
11
|
Mallory SA, Omar AK, Brady JF. Dynamic overlap concentration scale of active colloids. Phys Rev E 2021; 104:044612. [PMID: 34781543 DOI: 10.1103/physreve.104.044612] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2020] [Accepted: 10/06/2021] [Indexed: 11/07/2022]
Abstract
By introducing the notion of a dynamic overlap concentration scale, we identify additional universal features of the mechanical properties of active colloids. We codify these features by recognizing that the characteristic length scale of an active particle's trajectory, the run length, introduces a concentration scale ϕ^{*}. Large-scale simulations of repulsive active Brownian particles (ABPs) confirm that this run-length dependent concentration, the trajectory-space analog of the overlap concentration in polymer solutions, delineates distinct concentration regimes in which interparticle collisions alter particle trajectories. Using ϕ^{*} and concentration scales associated with colloidal jamming, the mechanical equation of state for ABPs collapses onto a set of principal curves that contain several overlooked features. The inclusion of these features qualitatively alters previous predictions of the behavior for active colloids, as we demonstrate by computing the spinodal for a suspension of purely repulsive ABPs. Our findings suggest that dynamic overlap concentration scales should help unravel the behavior of active and driven systems.
Collapse
Affiliation(s)
- Stewart A Mallory
- Department of Chemistry, The Pennsylvania State University, University Park, Pennyslvania 16802, USA
| | - Ahmad K Omar
- Department of Materials Science and Engineering, University of California, Berkeley, California 94720, USA
| | - John F Brady
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| |
Collapse
|
12
|
Gronchi G, Puglisi A. Optimization of an active heat engine. Phys Rev E 2021; 103:052134. [PMID: 34134299 DOI: 10.1103/physreve.103.052134] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2021] [Accepted: 05/05/2021] [Indexed: 12/15/2022]
Abstract
Optimization of heat engines at the microscale has applications in biological and artificial nanotechnology and stimulates theoretical research in nonequilibrium statistical physics. Here we consider noninteracting overdamped particles confined by an external harmonic potential, in contact with either a thermal reservoir or a stochastic self-propulsion force (active Ornstein-Uhlenbeck model). A cyclical machine is produced by periodic variation of the parameters of the potential and of the noise. An exact mapping between the passive and the active model allows us to define the effective temperature T_{eff}(t), which is meaningful for the thermodynamic performance of the engine. We show that T_{eff}(t) is different from all other known active temperatures, typically used in static situations. The mapping allows us to optimize the active engine, regardless of the values of the persistence time or self-propulsion velocity. In particular, through linear irreversible thermodynamics (small amplitude of the cycle), we give an explicit formula for the optimal cycle period and phase delay (between the two modulated parameters, stiffness and temperature) achieving maximum power with Curzon-Ahlborn efficiency. In the quasistatic limit, the formula for T_{eff}(t) simplifies and coincides with a recently proposed temperature for stochastic thermodynamics, bearing a compact expression for the maximum efficiency. A point, which has been overlooked in recent literature, is made about the difficulty in defining efficiency without a consistent definition of effective temperature.
Collapse
Affiliation(s)
- Giulia Gronchi
- Dipartimento di Fisica, Università di Roma Sapienza, Piazzale Aldo Moro 2, 00185 Rome, Italy
| | - Andrea Puglisi
- Dipartimento di Fisica, Università di Roma Sapienza, Piazzale Aldo Moro 2, 00185 Rome, Italy.,Istituto dei Sistemi Complessi, CNR, Piazzale Aldo Moro 5, 00185 Rome, Italy
| |
Collapse
|
13
|
Caprini L, Marini Bettolo Marconi U. Spatial velocity correlations in inertial systems of active Brownian particles. SOFT MATTER 2021; 17:4109-4121. [PMID: 33734261 DOI: 10.1039/d0sm02273j] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
Recently, it has been discovered that systems of active Brownian particles (APB) at high density organise their velocities into coherent domains showing large spatial structures in the velocity field. This collective behavior occurs spontaneously, i.e. is not caused by any specific interparticle force favoring the alignment of the velocities. This phenomenon was investigated in the absence of thermal noise and in the overdamped regime where inertial forces could be neglected. In this work, we demonstrate through numerical simulations and theoretical analysis that velocity alignment is a robust property of ABP and persists even in the presence of inertial forces and thermal fluctuations. We also show that a single dimensionless parameter, such as the Péclet number customarily employed in the description of self-propelled particles, is not sufficient to fully characterize this phenomenon either in the regimes of large viscosity or small mass. Indeed, the size of the velocity domains, measured through the correlation length of the spatial velocity correlation, remains constant when the swim velocity increases and decreases as the rotational diffusion becomes larger. We find that, contrary to the common belief, the spatial velocity correlation not only depends on inertia but is also non-symmetrically affected by mass and inverse viscosity variations. We conclude that in self-propelled systems, at variance with passive systems, variations in the inertial time (mass over solvent viscosity) and mass act as independent control parameters. Finally, we highlight the non-thermal nature of the spatial velocity correlations that are fairly insensitive both to solvent and active temperatures.
Collapse
Affiliation(s)
- Lorenzo Caprini
- School of Sciences and Technology, University of Camerino, Via Madonna delle Carceri, I-62032, Camerino, Italy.
| | | |
Collapse
|
14
|
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: 68] [Impact Index Per Article: 22.7] [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.
Collapse
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
| |
Collapse
|
15
|
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.
Collapse
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
| |
Collapse
|
16
|
Abstract
We investigate the non-equilibrium character of self-propelled particles through the study of the linear response of the active Ornstein–Uhlenbeck particle (AOUP) model. We express the linear response in terms of correlations computed in the absence of perturbations, proposing a particularly compact and readable fluctuation–dissipation relation (FDR): such an expression explicitly separates equilibrium and non-equilibrium contributions due to self-propulsion. As a case study, we consider non-interacting AOUP confined in single-well and double-well potentials. In the former case, we also unveil the effect of dimensionality, studying one-, two-, and three-dimensional dynamics. We show that information about the distance from equilibrium can be deduced from the FDR, putting in evidence the roles of position and velocity variables in the non-equilibrium relaxation.
Collapse
|
17
|
Caprini L, Marini Bettolo Marconi U. Active matter at high density: Velocity distribution and kinetic temperature. J Chem Phys 2020; 153:184901. [DOI: 10.1063/5.0029710] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Affiliation(s)
- Lorenzo Caprini
- Dipartimento di Fisica, Universitá di Camerino, Via Madonna delle Carceri, I-62032 Camerino, Italy
| | | |
Collapse
|
18
|
Lee JS, Park JM, Park H. Brownian heat engine with active reservoirs. Phys Rev E 2020; 102:032116. [PMID: 33075980 DOI: 10.1103/physreve.102.032116] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2020] [Accepted: 08/18/2020] [Indexed: 11/07/2022]
Abstract
Microorganisms such as bacteria are active matter which consume chemical energy and generate their unique run-and-tumble motion. A swarm of such microorganisms provide a nonequilibrium active environment whose noise characteristics are different from those of thermal equilibrium reservoirs. One important difference is a finite persistence time, which is considerably large compared to that of the equilibrium noise, that is, the active noise is colored. Here we study a mesoscopic energy-harvesting device (engine) with active reservoirs harnessing this noise nature. For an exactly solvable linear model, we show that the performance from the active environment can surpass that from the equilibrium environment. Furthermore, we propose a proper definition of the active-reservoir temperature and show that the engine efficiency can overcome the conventional Carnot bound, thus the power-efficiency trade-off constraint is released. We also show that the efficiency at the maximum power can surpass the Curzon-Ahlborn efficiency. This remarkable enhancement originates from the extra unconventional entropy production beyond the conventional Clausius entropy production, due to the non-Markovian nature of the active reservoirs. Interestingly, the supremacy of the active engine critically depends on the timescale symmetry of two active reservoirs.
Collapse
Affiliation(s)
- Jae Sung Lee
- School of Physics and Quantum Universe Center, Korea Institute for Advanced Study, Seoul 02455, Korea
| | - Jong-Min Park
- School of Physics and Quantum Universe Center, Korea Institute for Advanced Study, Seoul 02455, Korea
| | - Hyunggyu Park
- School of Physics and Quantum Universe Center, Korea Institute for Advanced Study, Seoul 02455, Korea
| |
Collapse
|
19
|
Flenner E, Szamel G. Active matter: Quantifying the departure from equilibrium. Phys Rev E 2020; 102:022607. [PMID: 32942354 DOI: 10.1103/physreve.102.022607] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2020] [Accepted: 07/28/2020] [Indexed: 11/07/2022]
Abstract
Active matter systems are driven out of equilibrium at the level of individual constituents. One widely studied class are systems of athermal particles that move under the combined influence of interparticle interactions and self-propulsions, with the latter evolving according to the Ornstein-Uhlenbeck stochastic process. Intuitively, these so-called active Ornstein-Uhlenbeck particle (AOUP) systems are farther from equilibrium for longer self-propulsion persistence times. Quantitatively, this is confirmed by the increasing equal-time velocity correlations (which are trivial in equilibrium) and by the increasing violation of the Einstein relation between the self-diffusion and mobility coefficients. In contrast, the entropy production rate, calculated from the ratio of the probabilities of the position space trajectory and its time-reversed counterpart, has a nonmonotonic dependence on the persistence time. Thus, it does not properly quantify the departure of AOUP systems from equilibrium.
Collapse
Affiliation(s)
- Elijah Flenner
- Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, USA
| | - Grzegorz Szamel
- Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, USA
| |
Collapse
|
20
|
Razin N. Entropy production of an active particle in a box. Phys Rev E 2020; 102:030103. [PMID: 33075964 DOI: 10.1103/physreve.102.030103] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2020] [Accepted: 09/09/2020] [Indexed: 06/11/2023]
Abstract
A run-and-tumble particle in a one-dimensional box (infinite potential well) is studied. The steady state is analytically solved and analyzed, revealing the emergent length scale of the boundary layer where particles accumulate near the walls. The mesoscopic steady state entropy production rate of the system is derived from coupled Fokker-Planck equations with a linear reaction term, resulting in an exact analytic expression. The entropy production density is shown to peak at the walls. Additionally, the derivative of the entropy production rate peaks at a system size proportional to the length scale of the accumulation boundary layer, suggesting that the behavior of the entropy production rate and its derivatives as a function of the control parameter may signify a qualitative behavior change in the physics of active systems, such as phase transitions.
Collapse
Affiliation(s)
- Nitzan Razin
- Division of Biology and Bioengineering, California Institute of Technology, Pasadena, California 91125, USA
| |
Collapse
|
21
|
Bickmann J, Wittkowski R. Predictive local field theory for interacting active Brownian spheres in two spatial dimensions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:214001. [PMID: 31791019 DOI: 10.1088/1361-648x/ab5e0e] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
We present a predictive local field theory for the nonequilibrium dynamics of interacting active Brownian particles with a spherical shape in two spatial dimensions. The theory is derived by a rigorous coarse-graining starting from the Langevin equations that describe the trajectories of the individual particles. For high accuracy and generality of the theory, it includes configurational order parameters and derivatives up to infinite order. In addition, we discuss possible approximations of the theory and present reduced models that are easier to apply. We show that our theory contains popular models such as Active Model B+ as special cases and that it provides explicit expressions for the coefficients occurring in these and other, often phenomenological, models. As a further outcome, the theory yields an analytical expression for the density-dependent mean swimming speed of the particles. To demonstrate an application of the new theory, we analyze a simple reduced model of the lowest nontrivial order in derivatives, which is able to predict the onset of motility-induced phase separation of the particles. By a linear stability analysis, an analytical expression for the spinodal corresponding to motility-induced phase separation is obtained. This expression is evaluated for the case of particles interacting repulsively by a Weeks-Chandler-Andersen potential. The analytical predictions for the spinodal associated with these particles are found to be in very good agreement with the results of Brownian dynamics simulations that are based on the same Langevin equations as our theory. Furthermore, the critical point predicted by our analytical results agrees excellently with recent computational results from the literature.
Collapse
Affiliation(s)
- Jens Bickmann
- Institut für Theoretische Physik, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, D-48149 Münster, Germany
| | | |
Collapse
|
22
|
Hanel R, Jizba P. Time-energy uncertainty principle for irreversible heat engines. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020; 378:20190171. [PMID: 32223412 PMCID: PMC7134951 DOI: 10.1098/rsta.2019.0171] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 11/26/2019] [Indexed: 05/28/2023]
Abstract
Even though irreversibility is one of the major hallmarks of any real-life process, an actual understanding of irreversible processes remains still mostly semi-empirical. In this paper, we formulate a thermodynamic uncertainty principle for irreversible heat engines operating with an ideal gas as a working medium. In particular, we show that the time needed to run through such an irreversible cycle multiplied by the irreversible work lost in the cycle is bounded from below by an irreducible and process-dependent constant that has the dimension of an action. The constant in question depends on a typical scale of the process and becomes comparable to Planck's constant at the length scale of the order Bohr radius, i.e. the scale that corresponds to the smallest distance on which the ideal gas paradigm realistically applies. This article is part of the theme issue 'Fundamental aspects of nonequilibrium thermodynamics'.
Collapse
Affiliation(s)
- Rudolf Hanel
- Section for Science of Complex Systems, Medical University of Vienna, Spitalgasse 23, Vienna 1090, Austria
| | - Petr Jizba
- FNSPE, Czech Technical University in Prague, Břehová 7, Praha 115 19, Czech Republic
| |
Collapse
|
23
|
Abstract
Large-scale collective behavior in suspensions of active particles can be understood from the balance of statistical forces emerging beyond the direct microscopic particle interactions. Here we review some aspects of the collective forces that can arise in suspensions of self-propelled active Brownian particles: wall forces under confinement, interfacial forces, and forces on immersed bodies mediated by the suspension. Even for non-aligning active particles, these forces are intimately related to a non-uniform polarization of particle orientations induced by walls and bodies, or inhomogeneous density profiles. We conclude by pointing out future directions and promising areas for the application of collective forces in synthetic active matter, as well as their role in living active matter.
Collapse
Affiliation(s)
- Thomas Speck
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany.
| |
Collapse
|
24
|
Omar AK, Wang ZG, Brady JF. Microscopic origins of the swim pressure and the anomalous surface tension of active matter. Phys Rev E 2020; 101:012604. [PMID: 32069575 DOI: 10.1103/physreve.101.012604] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2019] [Indexed: 06/10/2023]
Abstract
The unique pressure exerted by active particles-the "swim" pressure-has proven to be a useful quantity in explaining many of the seemingly confounding behaviors of active particles. However, its use has also resulted in some puzzling findings including an extremely negative surface tension between phase separated active particles. Here, we demonstrate that this contradiction stems from the fact that the swim pressure is not a true pressure. At a boundary or interface, the reduction in particle swimming generates a net active force density-an entirely self-generated body force. The pressure at the boundary, which was previously identified as the swim pressure, is in fact an elevated (relative to the bulk) value of the traditional particle pressure that is generated by this interfacial force density. Recognizing this unique mechanism for stress generation allows us to define a much more physically plausible surface tension. We clarify the utility of the swim pressure as an "equivalent pressure" (analogous to those defined from electrostatic and gravitational body forces) and the conditions in which this concept can be appropriately applied.
Collapse
Affiliation(s)
- Ahmad K Omar
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Zhen-Gang Wang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - John F Brady
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| |
Collapse
|
25
|
Caprini L, Hernández-García E, López C, Marini Bettolo Marconi U. A comparative study between two models of active cluster crystals. Sci Rep 2019; 9:16687. [PMID: 31723160 PMCID: PMC6853940 DOI: 10.1038/s41598-019-52420-1] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2019] [Accepted: 08/19/2019] [Indexed: 12/28/2022] Open
Abstract
We study a system of active particles with soft repulsive interactions that lead to an active cluster-crystal phase in two dimensions. We use two different modelizations of the active force - Active Brownian particles (ABP) and Ornstein-Uhlenbeck particles (AOUP) - and focus on analogies and differences between them. We study the different phases appearing in the system, in particular, the formation of ordered patterns drifting in space without being altered. We develop an effective description which captures some properties of the stable clusters for both ABP and AOUP. As an additional point, we confine such a system in a large channel, in order to study the interplay between the cluster crystal phase and the well-known accumulation near the walls, a phenomenology typical of active particles. For small activities, we find clusters attached to the walls and deformed, while for large values of the active force they collapse in stripes parallel to the walls.
Collapse
Affiliation(s)
- Lorenzo Caprini
- Gran Sasso Science Institute (GSSI), Via. F. Crispi 7, 67100, L'Aquila, Italy.
| | - Emilio Hernández-García
- IFISC (CSIC-UIB), Instituto de Física Interdisciplinar y Sistemas Complejos, Campus Universitat de les Illes Balears, E-07122, Palma de Mallorca, Spain
| | - Cristóbal López
- IFISC (CSIC-UIB), Instituto de Física Interdisciplinar y Sistemas Complejos, Campus Universitat de les Illes Balears, E-07122, Palma de Mallorca, Spain
| | | |
Collapse
|
26
|
Abstract
We propose a generalization of stochastic thermodynamics to systems of active particles, which move under the combined influence of stochastic internal self-propulsions (activity) and a heat bath. The main idea is to consider joint trajectories of particles' positions and self-propulsions. It is then possible to exploit formal similarity of an active system and a system consisting of two subsystems interacting with different heat reservoirs and coupled by a nonsymmetric interaction. The resulting thermodynamic description closely follows the standard stochastic thermodynamics. In particular, total entropy production, Δs_{tot}, can be decomposed into housekeeping, Δs_{hk}, and excess, Δs_{ex}, parts. Both Δs_{tot} and Δs_{hk} satisfy fluctuation theorems. The average rate of the steady-state housekeeping entropy production can be related to the violation of the fluctuation-dissipation theorem via a Harada-Sasa relation. The excess entropy production enters into a Hatano-Sasa-like relation, which leads to a generalized Clausius inequality involving the change of the system's entropy and the excess entropy production. Interestingly, although the evolution of particles' self-propulsions is free and uncoupled from that of their positions, nontrivial steady-state correlations between these variables lead to the nonzero excess dissipation in the reservoir coupled to the self-propulsions.
Collapse
Affiliation(s)
- Grzegorz Szamel
- Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, USA
| |
Collapse
|
27
|
Sevilla FJ, Rodríguez RF, Gomez-Solano JR. Generalized Ornstein-Uhlenbeck model for active motion. Phys Rev E 2019; 100:032123. [PMID: 31640041 DOI: 10.1103/physreve.100.032123] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2019] [Indexed: 06/10/2023]
Abstract
We investigate a one-dimensional model of active motion, which takes into account the effects of persistent self-propulsion through a memory function in a dissipative-like term of the generalized Langevin equation for particle swimming velocity. The proposed model is a generalization of the active Ornstein-Uhlenbeck model introduced by G. Szamel [Phys. Rev. E 90, 012111 (2014)10.1103/PhysRevE.90.012111]. We focus on two different kinds of memory which arise in many natural systems: an exponential decay and a power law, supplemented with additive colored noise. We provide analytical expressions for the velocity autocorrelation function and the mean-squared displacement, which are in excellent agreement with numerical simulations. For both models, damped oscillatory solutions emerge due to the competition between the memory of the system and the persistence of velocity fluctuations. In particular, for a power-law model with fractional Brownian noise, we show that long-time active subdiffusion occurs with increasing long-term memory.
Collapse
Affiliation(s)
- Francisco J Sevilla
- Departamento de Sistemas Complejos, Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, 01000, Ciudad de México, México
| | - Rosalío F Rodríguez
- Departamento de Sistemas Complejos, Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, 01000, Ciudad de México, México
- FENOMEC, Universidad Nacional Autónoma de México, Apdo. Postal 20-726, 01000, Ciudad de México, México
| | - Juan Ruben Gomez-Solano
- Departamento de Sistemas Complejos, Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, 01000, Ciudad de México, México
| |
Collapse
|
28
|
Caprini L, Cecconi F, Marini Bettolo Marconi U. Transport of active particles in an open-wedge channel. J Chem Phys 2019; 150:144903. [DOI: 10.1063/1.5090104] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Lorenzo Caprini
- Gran Sasso Science Institute (GSSI), Via F.Crispi 7, I-67100 L’Aquila, Italy
| | - Fabio Cecconi
- Istituto dei Sistemi Complessi (CNR), Via Taurini 19, I-00185 Roma, Italy
| | | |
Collapse
|
29
|
Probability Distributions with Singularities. ENTROPY 2019; 21:e21030312. [PMID: 33267026 PMCID: PMC7514793 DOI: 10.3390/e21030312] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/28/2019] [Revised: 03/19/2019] [Accepted: 03/20/2019] [Indexed: 11/30/2022]
Abstract
In this paper we review some general properties of probability distributions which exhibit a singular behavior. After introducing the matter with several examples based on various models of statistical mechanics, we discuss, with the help of such paradigms, the underlying mathematical mechanism producing the singularity and other topics such as the condensation of fluctuations, the relationships with ordinary phase-transitions, the giant response associated to anomalous fluctuations, and the interplay with fluctuation relations.
Collapse
|
30
|
Caprini L, Marini Bettolo Marconi U. Active chiral particles under confinement: surface currents and bulk accumulation phenomena. SOFT MATTER 2019; 15:2627-2637. [PMID: 30810571 DOI: 10.1039/c8sm02492h] [Citation(s) in RCA: 39] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
In this work, we study the stationary behavior of an assembly of independent chiral active particles under confinement by employing an extension of the active Ornstein-Uhlenbeck model. The chirality modeled by means of an effective torque term leads to a drastic reduction in the accumulation near the walls with respect to the case without handedness and to the appearance of currents parallel to the container walls accompanied by a large accumulation of particles in the inner region. In the case of two-dimensional chiral particles confined by harmonic walls, we determine the analytic form of the distribution of positions and velocities in two different situations: a rotationally invariant confining potential and an infinite channel with parabolic walls. Both these models display currents and chirality induced inner accumulation. These phenomena are further investigated by means of a more realistic description of a channel, where the wall and bulk regions are clearly separated. The corresponding current and density profiles are obtained by numerical simulations. At variance with the harmonic models, the third model shows a progressive emptying of the wall regions and the simultaneous enhancement of the bulk population. We explain such a phenomenon in terms of the combined effect of wall repulsive forces and chiral motion and provide a semiquantitative description of the current profile in terms of effective viscosity of the chiral gas.
Collapse
Affiliation(s)
- Lorenzo Caprini
- Gran Sasso Science Institute (GSSI), Via. F. Crispi 7, 67100 L'Aquila, Italy
| | | |
Collapse
|
31
|
Fischer A, Chatterjee A, Speck T. Aggregation and sedimentation of active Brownian particles at constant affinity. J Chem Phys 2019; 150:064910. [PMID: 30769983 DOI: 10.1063/1.5081115] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
Affiliation(s)
- Andreas Fischer
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
- Graduate School Materials Science in Mainz, Staudinger Weg 9, 55128 Mainz, Germany
| | - Arkya Chatterjee
- Department of Physics, Indian Institute of Technology-Bombay, Powai, Mumbai 400076, India
| | - Thomas Speck
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
| |
Collapse
|
32
|
Caprini L, Marini Bettolo Marconi U, Puglisi A. Activity induced delocalization and freezing in self-propelled systems. Sci Rep 2019; 9:1386. [PMID: 30718579 PMCID: PMC6361910 DOI: 10.1038/s41598-018-36824-z] [Citation(s) in RCA: 33] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2018] [Accepted: 11/23/2018] [Indexed: 11/08/2022] Open
Abstract
We study a system of interacting active particles, propelled by colored noises, characterized by an activity time τ, and confined by a single-well anharmonic potential. We assume pair-wise repulsive forces among particles, modelling the steric interactions among microswimmers. This system has been experimentally studied in the case of a dilute suspension of Janus particles confined through acoustic traps. We observe that already in the dilute regime - when inter-particle interactions are negligible - increasing the persistent time, τ, pushes the particles away from the potential minimum, until a saturation distance is reached. We compute the phase diagram (activity versus interaction length), showing that the interaction does not suppress this delocalization phenomenon but induces a liquid- or solid-like structure in the densest regions. Interestingly a reentrant behavior is observed: a first increase of τ from small values acts as an effective warming, favouring fluidization; at higher values, when the delocalization occurs, a further increase of τ induces freezing inside the densest regions. An approximate analytical scheme gives fair predictions for the density profiles in the weakly interacting case. The analysis of non-equilibrium heat fluxes reveals that in the region of largest particle concentration equilibrium is restored in several aspects.
Collapse
Affiliation(s)
- Lorenzo Caprini
- Gran Sasso Science Institute (GSSI), Via. F. Crispi 7, 67100, L'Aquila, Italy.
| | | | - Andrea Puglisi
- Istituto dei Sistemi Complessi - CNR and Dipartimento di Fisica, Università di Roma Sapienza, P.le Aldo Moro 2, 00185, Rome, Italy
| |
Collapse
|
33
|
Nemoto T, Fodor É, Cates ME, Jack RL, Tailleur J. Optimizing active work: Dynamical phase transitions, collective motion, and jamming. Phys Rev E 2019; 99:022605. [PMID: 30934223 DOI: 10.1103/physreve.99.022605] [Citation(s) in RCA: 38] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2018] [Indexed: 06/09/2023]
Abstract
Active work measures how far the local self-forcing of active particles translates into real motion. Using population Monte Carlo methods, we investigate large deviations in the active work for repulsive active Brownian disks. Minimizing the active work generically results in dynamical arrest; in contrast, despite the lack of aligning interactions, trajectories of high active work correspond to a collectively moving, aligned state. We use heuristic and analytic arguments to explain the origin of dynamical phase transitions separating the arrested, typical, and aligned regimes.
Collapse
Affiliation(s)
- Takahiro Nemoto
- Philippe Meyer Institute for Theoretical Physics, Physics Department, École Normale Supérieure & PSL Research University, 24 rue Lhomond, 75231 Paris Cedex 05, France
| | - Étienne Fodor
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - 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
| | - Julien Tailleur
- Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS/P7, Université Paris Diderot, 10 rue Alice Domon et Léonie Duquet, 75205 Paris cedex 13, France
| |
Collapse
|
34
|
Caprini L, Marini Bettolo Marconi U, Puglisi A, Vulpiani A. Active escape dynamics: The effect of persistence on barrier crossing. J Chem Phys 2019; 150:024902. [DOI: 10.1063/1.5080537] [Citation(s) in RCA: 39] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Lorenzo Caprini
- Gran Sasso Science Institute (GSSI), Via. F. Crispi 7, 67100 L’Aquila, Italy
| | - Umberto Marini Bettolo Marconi
- Scuola di Scienze e Tecnologie, Università di Camerino, Via Madonna delle Carceri, 62032 Camerino, Italy and INFN, Perugia, Italy
| | - Andrea Puglisi
- CNR-ISC, Consiglio Nazionale delle Ricerche, Dipartimento di Fisica, Università La Sapienza, P.le A. Moro 2, 00185 Rome, Italy
| | - Angelo Vulpiani
- Dipartimento di Fisica, Università di Roma Sapienza, I-00185 Rome, Italy
| |
Collapse
|
35
|
Caprini L, Marini Bettolo Marconi U. Active particles under confinement and effective force generation among surfaces. SOFT MATTER 2018; 14:9044-9054. [PMID: 30387799 DOI: 10.1039/c8sm01840e] [Citation(s) in RCA: 47] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We consider the effect of geometric confinement on the steady-state properties of a one-dimensional active suspension subject to thermal noise. The random active force is modeled by an Ornstein-Uhlenbeck process and the system is studied both numerically, by integrating the Langevin governing equations, and analytically by solving the associated Fokker-Planck equation under suitable approximations. The comparison between the two approaches displays a fairly good agreement and in particular, we show that the Fokker-Planck approach can predict the structure of the system both in the wall region and in the bulk-like region where the surface forces are negligible. The simultaneous presence of thermal noise and active forces determines the formation of a layer, extending from the walls towards the bulk, where the system exhibits polar order. We relate the presence of such ordering to the mechanical pressure exerted on the container's walls and show how it depends on the separation of the boundaries and determines a Casimir-like attractive force mediated by the active suspension.
Collapse
Affiliation(s)
- Lorenzo Caprini
- Gran Sasso Science Institute (GSSI), Via. F. Crispi 7, 67100 L'Aquila, Italy
| | | |
Collapse
|
36
|
Shankar S, Marchetti MC. Hidden entropy production and work fluctuations in an ideal active gas. Phys Rev E 2018; 98:020604. [PMID: 30253539 DOI: 10.1103/physreve.98.020604] [Citation(s) in RCA: 55] [Impact Index Per Article: 9.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2018] [Indexed: 11/07/2022]
Abstract
Collections of self-propelled particles that move persistently by continuously consuming free energy are a paradigmatic example of active matter. In these systems, unlike Brownian "hot colloids," the breakdown of detailed balance yields a continuous production of entropy at steady state, even for an ideal active gas. We quantify the irreversibility for a noninteracting active particle in two dimensions by treating both conjugated and time-reversed dynamics. By starting with underdamped dynamics, we identify a hidden rate of entropy production required to maintain persistence and prevent the rapidly relaxing momenta from thermalizing, even in the limit of very large friction. Additionally, comparing two popular models of self-propulsion with identical dissipation on average, we find that the fluctuations and large deviations in work done are markedly different, providing thermodynamic insight into the varying extents to which macroscopically similar active matter systems may depart from equilibrium.
Collapse
Affiliation(s)
- Suraj Shankar
- Physics Department and Syracuse Soft and Living Matter Program, Syracuse University, Syracuse, New York 13244, USA.,and Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
| | - M Cristina Marchetti
- Physics Department and Syracuse Soft and Living Matter Program, Syracuse University, Syracuse, New York 13244, USA.,and Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
| |
Collapse
|
37
|
Caprini L, Marconi UMB, Puglisi A, Vulpiani A. Comment on "Entropy Production and Fluctuation Theorems for Active Matter". PHYSICAL REVIEW LETTERS 2018; 121:139801. [PMID: 30312080 DOI: 10.1103/physrevlett.121.139801] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/05/2018] [Indexed: 06/08/2023]
Affiliation(s)
- Lorenzo Caprini
- Gran Sasso Science Institute (GSSI), Via F. Crispi 7, 67100 L'Aquila, Italy
| | | | - Andrea Puglisi
- Istituto dei Sistemi Complessi, CNR and Dipartimento di Fisica, Università di Roma Sapienza, Piazza le Aldo Moro 2, 00185 Rome, Italy
| | - Angelo Vulpiani
- Dipartimento di Fisica, Università Sapienza, Piazza le A. Moro 2, 00185 Roma, Italy and Centro Interdisciplinare "B. Segre," Accademia dei Lincei, 00165 Roma, Italy
| |
Collapse
|
38
|
Mandal D, Klymko K, DeWeese MR. Mandal, Klymko, and DeWeese Reply. PHYSICAL REVIEW LETTERS 2018; 121:139802. [PMID: 30312081 DOI: 10.1103/physrevlett.121.139802] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2018] [Indexed: 06/08/2023]
Affiliation(s)
- Dibyendu Mandal
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Katherine Klymko
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Michael R DeWeese
- Department of Physics, University of California, Berkeley, California 94720, USA
- Redwood Center for Theoretical Neuroscience and Helen Wills Neuroscience Institute, University of California, Berkeley, California 94720, USA
| |
Collapse
|
39
|
|
40
|
Wang Z, Chen YF, Chen HY, Sheng YJ, Tsao HK. Mechanical pressure, surface excess, and polar order of a dilute rod-like nanoswimmer suspension: role of swimmer-wall interactions. SOFT MATTER 2018; 14:2906-2914. [PMID: 29589848 DOI: 10.1039/c7sm02372c] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
The mechanical pressure, surface excess, and polar order of a dilute rod-like nanoswimmer suspension confined by two parallel plates are explored by dissipative particle dynamics. The accumulation and preferred orientation of swimmers near the walls are distinctly shown through the density and polar order distributions for various active force, Fa, values and rod lengths. As Fa is increased, it is interesting to observe that there exists a maximum of the polar order, revealing that the dominant mechanism of the swimmer behavior can be altered by the coupling between the active force and the rod-wall interaction. As a result, the influences of the active force on the swim pressure Π(w)a contributed by the swimmers directly and the surface excess Γ* can be classified into two scaling regimes, natural rotation (weak propulsion) and forced rotation (strong propulsion). Π(w)a and Γ* are proportional to Fa2 in the former regime but become proportional to Fa in the latter regime. For all rod-wall repulsions, the swim pressure of active rods in confined systems Π(w)a always differs from that in unbounded systems Π(b)a which is simply proportional to Fa2 associated with the active diffusivity. That is, unlike thermal equilibrium systems, Π(w)a is not a state function because of the presence of the wall-torque.
Collapse
Affiliation(s)
- Zhengjia Wang
- Condensed Matter Science and Technology Institute, School of Science, Harbin Institute of Technology, Harbin 150080, People's Republic of China
| | | | | | | | | |
Collapse
|
41
|
Marini Bettolo Marconi U, Sarracino A, Maggi C, Puglisi A. Self-propulsion against a moving membrane: Enhanced accumulation and drag force. Phys Rev E 2018; 96:032601. [PMID: 29347004 DOI: 10.1103/physreve.96.032601] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2017] [Indexed: 11/07/2022]
Abstract
Self-propulsion (SP) is a main feature of active particles (AP), such as bacteria or biological micromotors, distinguishing them from passive colloids. A renowned consequence of SP is accumulation at static interfaces, even in the absence of hydrodynamic interactions. Here we address the role of SP in the interaction between AP and a moving semipermeable membrane. In particular, we implement a model of noninteracting AP in a channel crossed by a partially penetrable wall, moving at a constant velocity c. With respect to both the cases of passive colloids with c>0 and AP with c=0, the AP with finite c show enhancement of accumulation in front of the obstacle and experience a largely increased drag force. This effect is understood in terms of an effective potential localised at the interface between particles and membrane, of height proportional to cτ/ξ, where τ is the AP's reorientation time and ξ the width characterizing the surface's smoothness (ξ→0 for hard core obstacles). An approximate analytical scheme is able to reproduce the observed density profiles and the measured drag force, in very good agreement with numerical simulations. The effects discussed here can be exploited for automatic selection and filtering of AP with desired parameters.
Collapse
Affiliation(s)
- U Marini Bettolo Marconi
- Scuola di Scienze e Tecnologie, Università di Camerino, Via Madonna delle Carceri, 62032, Camerino, INFN Perugia, Italy
| | - A Sarracino
- CNR-ISC and Dipartimento di Fisica, Sapienza Università di Roma, p.le A. Moro 2, 00185 Roma, Italy
| | - C Maggi
- CNR-NANOTEC and Dipartimento di Fisica, Sapienza Università di Roma, p.le A. Moro 2, 00185 Roma, Italy
| | - A Puglisi
- CNR-ISC and Dipartimento di Fisica, Sapienza Università di Roma, p.le A. Moro 2, 00185 Roma, Italy
| |
Collapse
|
42
|
Mandal D, Klymko K, DeWeese MR. Entropy Production and Fluctuation Theorems for Active Matter. PHYSICAL REVIEW LETTERS 2017; 119:258001. [PMID: 29303303 DOI: 10.1103/physrevlett.119.258001] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2017] [Indexed: 05/18/2023]
Abstract
Active biological systems reside far from equilibrium, dissipating heat even in their steady state, thus requiring an extension of conventional equilibrium thermodynamics and statistical mechanics. In this Letter, we have extended the emerging framework of stochastic thermodynamics to active matter. In particular, for the active Ornstein-Uhlenbeck model, we have provided consistent definitions of thermodynamic quantities such as work, energy, heat, entropy, and entropy production at the level of single, stochastic trajectories and derived related fluctuation relations. We have developed a generalization of the Clausius inequality, which is valid even in the presence of the non-Hamiltonian dynamics underlying active matter systems. We have illustrated our results with explicit numerical studies.
Collapse
Affiliation(s)
- Dibyendu Mandal
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Katherine Klymko
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Michael R DeWeese
- Department of Physics, University of California, Berkeley, California 94720, USA
- Redwood Center for Theoretical Neuroscience and Helen Wills Neuroscience Institute, University of California, Berkeley, California 94720, USA
| |
Collapse
|
43
|
Marini Bettolo Marconi U, Maggi C, Paoluzzi M. Pressure in an exactly solvable model of active fluid. J Chem Phys 2017; 147:024903. [DOI: 10.1063/1.4991731] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | - Claudio Maggi
- NANOTEC-CNR, Institute of Nanotechnology, Soft and Living Matter Laboratory, Piazzale A. Moro 2, I-00185 Roma, Italy
| | - Matteo Paoluzzi
- Department of Physics, Syracuse University, Syracuse, New York 13244, USA
| |
Collapse
|
44
|
Clausius Relation for Active Particles: What Can We Learn from Fluctuations. ENTROPY 2017. [DOI: 10.3390/e19070356] [Citation(s) in RCA: 37] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|