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 non-symmetric interaction. The resulting thermodynamic description closely follows the standard stochastic thermodynamics. In particular, total entropy production, $Δs_\text{tot}$, can be decomposed into housekeeping, $Δs_\text{hk}$, and excess, $Δs_\text{ex}$, parts. Both $Δs_\text{tot}$ and $Δs_\text{hk}$ 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, non-trivial steady-state correlations between these variables lead to the non-zero excess dissipation in the reservoir coupled to the self-propulsions.
Motility-induced phase separation (MIPS) arises generically in fluids of self-propelled particles when interactions lead to a kinetic slowdown at high densities. Starting from a continuum description of scalar active matter, akin to a generalized Cahn-Hilliard equation, we give a general prescription for the mean densities of coexisting phases in flux-free steady states that amounts, at a hydrodynamics scale, to extremizing an effective free energy. We illustrate our approach on two well-known models: self-propelled particles interacting either through a density-dependent propulsion speed or v…
We present a comprehensive study of Vicsek-style self-propelled particle models in two and three space dimensions. The onset of collective motion in such stochastic models with only local alignment interactions is studied in detail and shown to be discontinuous (first-order like). The properties of the ordered, collectively moving phase are investigated. In a large domain of parameter space including the transition region, well-defined high-density and high-order propagating solitary structures are shown to dominate the dynamics. Far enough from the transition region, on the other hand, these …
In this work, the dynamics of a self-propelled stochastic particle under the influence of an axisymmetric light field was experimentally studied. The particle under consideration has the main characteristic of carrying a light sensor in an eccentric location. For the chosen experimental conditions, the emerging trajectories were orbital, and, more interestingly, they presented two preferential radial distances. A mathematical model incorporating the key experimental components was introduced. By means of numerical simulations and theoretical analysis, it was found that, in addition to the orbi…
Many self-propelled objects are large enough to exhibit inertial effects but still suffer from environmental fluctuations. The corresponding basic equations of motion are governed by active Langevin dynamics which involve inertia, friction and stochastic noise for both the translational and orientational degrees of freedom coupled via the self-propulsion along the particle orientation. In this paper, we generalize the active Langevin model to time-dependent parameters and explicitly discuss the effect of time-dependent inertia for achiral and chiral particles. Realizations of this situation ar…
Directed transport of interacting active (self-propelled)Brownian particles is numerically investigated in confined geometries (entropic barriers). The self-propelled velocity can break thermodynamical equilibrium and induce the directed transport. It is found that the interaction between active particles can greatly affect the ratchet transport. For attractive particles, on increasing the interaction strength, the average velocity firstly decreases to its minima, then increases, and finally decreases to zero. For repulsive particles, when the interaction is very weak, there exists a critical …
Self-propelled particles phase separate into coexisting dense and dilute regions above a critical density. The statistical nature of their stochastic motion lends itself to various theories that predict the onset of phase separation. However, these theories are ill equipped to describe such behavior when noise become negligible. To overcome this limitation, we present a predictive model that relies on two density-dependent timescales: $τ_F$, the mean time particles spend between collisions; and $τ_C$, the mean lifetime of a collision. We show that only when $τ_F < τ_C$ do collisions last long …
We study collections of self-propelled rods (SPR) moving in two dimensions for packing fractions less than or equal to 0.3. We find that in the thermodynamical limit the SPR undergo a phase transition between a disordered gas and a novel phase-separated system state. Interestingly, (global) orientational order patterns -- contrary to what has been suggested -- vanish in this limit. In the found novel state, the SPR self-organize into a highly dynamical, high-density, compact region - which we call aggregate - which is surrounded by a disordered gas. Active stresses build inside aggregates as r…
We study a set of models of self-propelled particles that achieve collective motion through similar alignment-based dynamics, considering versions with and without repulsive interactions that do not affect the heading directions. We explore their phase space within a broad range of values of two nondimensional parameters (coupling strength and Peclet number), characterizing their polarization and degree of clustering. The resulting phase diagrams display equivalent, similarly distributed regions for all models with repulsion. The diagrams without repulsion exhibit differences, in particular fo…
Université Paris-Saclay（巴黎萨克雷大学）；CNRS（法国国家科学研究中心）；FAST（快速科学与技术实验室）；Sorbonne Université（索邦大学）；Physicochimie des Electrolytes et Nanosystèmes Interfaciaux（电解质与界面纳米系统物理化学）；University of Pennsylvania（宾夕法尼亚大学）
We study the glassy dynamics taking place in dense assemblies of athermal active particles that are driven solely by a nonequilibrium self-propulsion mechanism. Active forces are modeled as an Ornstein-Uhlenbeck stochastic process, characterized by a persistence time and an effective temperature, and particles interact via a Lennard-Jones potential that yields well-studied glassy behavior in the Brownian limit, obtained as the persistence time vanishes. By increasing the persistence time, the system departs more strongly from thermal equilibrium and we provide a comprehensive numerical analysi…
A model of self-driven particles similar to the Vicsek model [Phys. Rev. Lett. 75 (1995) 1226] but with metric-free interactions is studied by means of a novel Enskog-type kinetic theory. In this model, N particles of constant speed v0 try to align their travel directions with the average direction of a fixed number of closest neighbors. At strong alignment a global flocking state forms. The alignment is defined by a stochastic rule, not by a Hamiltonian. The corresponding interactions are of genuine multi-body nature. The theory is based on a Master equation in 3N-dimensional phase space, whi…
Miniaturized, self-propelled locomotors use chemo-mechanical transduction mechanisms to convert fuel in the environment to autonomous motion. Recent experimental and theoretical studies demonstrate that these autonomous engines can passively follow the contours of solid boundaries they encounter. Boundary guidance, however, is not necessarily stable: Mechanical disturbances can cause the motor to hydrodynamically depart from the passively guided pathway. Furthermore, given the scaled-down size of micromotors (typically 100 nm -10 $μ$m), Brownian thermal fluctuation forces are necessarily impor…
Self-propelled particles include both self-phoretic synthetic colloids and various micro-organisms. By continually consuming energy, they bypass the laws of equilibrium thermodynamics. These laws enforce the Boltzmann distribution in thermal equilibrium: the steady state is then independent of kinetic parameters. In contrast, self-propelled particles tend to accumulate where they move more slowly. They may also slow down at high density, for either biochemical or steric reasons. This creates positive feedback which can lead to motility-induced phase separation (MIPS) between dense and dilute f…
Active diffusiophoresis - swimming through interaction with a self-generated, neutral, solute gradient - is a paradigm for autonomous motion at the micrometer scale. We study this propulsion mechanism within a linear response theory. Firstly, we consider several aspects relating to the dynamics of the swimming particle. We extend established analytical formulae to describe small swimmers, which interact with their environment on a finite lengthscale. Solute convection is also taken into account. Modeling of the chemical reaction reveals a coupling between the angular distribution of reactivity…
Seifert derived an exact fluctuation relation for diffusion processes using the concept of "stochastic system entropy". In this note we extend his formalism to entropic transport. We introduce the notion of relative stochastic entropy, or "relative surprisal", and use it to generalize Seifert's system/medium decomposition of the total entropy. This result allows to apply the concepts of stochastic thermodynamics to diffusion processes in confined geometries, such as ion channels, cellular pores or nanoporous materials. It can be seen as the equivalent for diffusion processes of Esposito and Sc…
The propulsion of active particles by self-diffusiophoresis is driven by asymmetric catalytic reactions on the particle surface that generate a mechanochemical coupling between the fluid velocity and the concentration fields of fuel and product in the surrounding solution. Because of thermal and molecular fluctuations in the solution, the motion of micrometric or submicrometric active particles is stochastic. Coupled Langevin equations describing the translation, rotation, and reaction of such active particles are deduced from fluctuating chemohydrodynamics and fluctuating boundary conditions …
Rectified transport of active ellipsoidal particles is numerically investigated in a two-dimensional asymmetric potential. The out-of-equilibrium condition for the active particle is an intrinsic property, which can break thermodynamical equilibrium and induce the directed transport. It is found that the perfect sphere particle can facilitate the rectification, while the needlelike particle destroys the directed transport. There exist optimized values of the parameters (the self-propelled velocity, the torque acting on the body) at which the average velocity takes its maximal value. For the el…
In Part I of this two-part series, the reverse perturbation method for shearing simple liquids [Phys. Rev. E 59, 4894 (1999)] was extended to systems of interacting particles with time-discrete stochastic dynamics. For verification, in this paper (Part II) the reverse perturbation method is first applied to a simple momentum-conserving liquid, modeled through the Multi-Particle Collision Dynamics (MPCD) technique [J. Chem. Phys. 110, 8605 (1999)]. For MPCD, excellent agreement between the measured shear viscosity and its theoretical prediction is found. Furthermore, this paper contains applica…
Stochastic thermodynamics provides a framework for describing small systems like colloids or biomolecules driven out of equilibrium but still in contact with a heat bath. Both, a first-law like energy balance involving exchanged heat and entropy production entering refinements of the second law can consistently be defined along single stochastic trajectories. Various exact relations involving the distribution of such quantities like integral and detailed fluctuation theorems for total entropy production and the Jarzynski relation follow from such an approach based on Langevin dynamics. Analogu…
As technological advances allow us to fabricate smaller autonomous self-propelled devices, it is clear that at some point directed propulsion could not come from pre-specified deterministic periodic deformation of the swimmer's body and we need to develop strategies to extract a net directed motion from a series of random transitions in the conformation space of the swimmer. We present a theoretical formulation to describe the "stochastic motor" that drives the motion of low Reynolds number swimmers based on this concept, and use it to study the propulsion of a simple low Reynolds number swimm…
Topological protection has emerged as an organizing principle for understanding and engineering robust collective behavior in electronic and material systems. Recent work suggests that topology may also play a role in organizing stochastic processes relevant to biology and self-assembly. Here, we show that topological protection in chemical networks can be understood entirely in terms of nonequilibrium thermodynamics. We illustrate these ideas using simple examples inspired by the literature.
Self-propelled particles with hydrodynamic interactions (microswimmers) have previously been shown to produce long-range ordering phenomena. Many theoretical explanations for these collective phenomena are connected to instabilities in the hydrodynamic or kinetic equations. By incorporating stochastic fluxes into the mean field kinetic equation, we quantify the dynamics of a suspension of microswimmers in the parameter regime where the deterministic equation is stable. We can thereby compute nontrivial collective phenomena concerning spatial correlations of orientation and stress as well as th…
The diffusion properties of self-propelled particles which move at constant speed and, in addition, reverse their direction of motion repeatedly are investigated. The internal dynamics of particles triggering these reversal processes is modeled by a stochastic clock. The velocity correlation function as well as the mean squared displacement is investigated and, furthermore, a general expression for the diffusion coefficient for self-propelled particles with directional reversal is derived. Our analysis reveals the existence of an optimal, finite rotational noise amplitude which maximizes the d…
Hydrodynamical interactions of active micro-particles are pervasive in our planet's fluid environments. Hence, understanding the interactions of these self-propelled particles is essential for science and engineering. In this paper the suspensions of active swimmer-rotor particles have been mathematically modeled by extending a previously developed stochastic kinetic theory to analyze heterogeneous collections of microswimmers and microrotors with multiple spin velocity populations. The paper uses this modeling approach to derive insights on large scale properties such as suspension instabilit…
We study the problem of optimizing released heat or dissipated work in stochastic thermodynamics. In the overdamped limit these functionals have singular solutions, previously interpreted as protocol jumps. We show that a regularization, penalizing a properly defined acceleration, changes the jumps into boundary layers of finite width. We show that in the limit of vanishing boundary layer width no heat is dissipated in the boundary layer, while work can be done. We further give a new interpretation of the fact that the optimal protocols in the overdamped limit are given by optimal deterministi…
For configurational changes of soft matter systems affected or caused by external hydrodynamic flow, we identify applied work, exchanged heat, and entropy change on the level of a single trajectory. These expressions guarantee invariance of stochastic thermodynamics under a change of frame of reference. As criterion for equilibrium \textit{vs.} nonequilibrium, zero \textit{vs.} nonzero applied work replaces detailed balance \textit{vs.} nonvanishing currents, since both latter criteria are shown to depend on the frame of reference. Our results are illustrated quantitatively by calculating the …
Recent studies aimed at investigating artificial analogs of bacterial colonies have shown that low-density suspensions of self-propelled particles confined in two dimensions can assemble into finite aggregates that merge and split, but have a typical size that remains constant (living clusters). In this Letter we address the problem of the formation of living clusters and crystals of active particles in three dimensions. We study two systems: self-propelled particles interacting via a generic attractive potential and colloids that can move towards each other as a result of active agents (e.g. …
Technische Universität Dresden（德累斯顿工业大学）；Max Planck Institute of Molecular Cell Biology and Genetics（马克斯·普朗克分子细胞生物学与遗传学研究所）；Center for Systems Biology Dresden（德累斯顿系统生物学中心）；Center for Scalable Data Analytics and Artificial Intelligence ScaDS.AI（可扩展数据分析与人工智能中心 ScaDS.AI）；Cluster of Excellence Physics of Life, TU Dresden（德累斯顿工业大学生命物理卓越集群）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；University of Geneva（日内瓦大学）
We present a principled data-driven strategy for learning deterministic hydrodynamic models directly from stochastic non-equilibrium active particle trajectories. We apply our method to learning a hydrodynamic model for the propagating density lanes observed in self-propelled particle systems and to learning a continuum description of cell dynamics in epithelial tissues. We also infer from stochastic particle trajectories the latent phoretic fields driving chemotaxis. This demonstrates that statistical learning theory combined with physical priors can enable discovery of multi-scale models of …
