Origins and diagnostics of the nonequilibrium character of active systems (original) (raw)
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Clausius Relation for Active Particles: What Can We Learn from Fluctuations
Entropy, 2017
Many kinds of active particles, such as bacteria or active colloids, move in a thermostatted fluid by means of self-propulsion. Energy injected by such a non-equilibrium force is eventually dissipated as heat in the thermostat. Since thermal fluctuations are much faster and weaker than self-propulsion forces, they are often neglected, blurring the identification of dissipated heat in theoretical models. For the same reason, some freedom-or arbitrariness-appears when defining entropy production. Recently three different recipes to define heat and entropy production have been proposed for the same model where the role of self-propulsion is played by a Gaussian coloured noise. Here we compare and discuss the relation between such proposals and their physical meaning. One of these proposals takes into account the heat exchanged with a non-equilibrium active bath: such an "active heat" satisfies the original Clausius relation and can be experimentally verified.
The Journal of Chemical Physics, 1998
Within the scope of a nonequilibrium statistical ensemble formalism we derive a hierarchy of equations of evolution for a set of basic thermo-hydrodynamic variables, which describe the macroscopic nonequilibrium state of a fluid of bosons. This set is composed of the energy density and number density and their fluxes of all order. The resulting equations can be considered as far-reaching generalizations of those in Mori's approach. They involve nonlocality in space and retro-effects ͑i.e. correlations in space and time respectively͒, are highly nonlinear, and account for irreversible behavior in the macroscopic evolution of the system. The different contributions to these kinetic equations are analyzed and the Markovian limit is obtained. In the follow up article we consider the nonequilibrium thermodynamic properties that the formalism provides.
Nonequilibrium steady states in Langevin thermal systems
Physical Review E
Equilibrium is characterized by its fundamental properties such as the detailed balance, the fluctuation-dissipation relation, and no heat dissipation. Based on the stochastic thermodynamics, we show that these three properties are equivalent to each other in conventional Langevin thermal systems with microscopic reversibility. Thus, a conventional steady state has either all three properties (equilibrium) or none of them (nonequilibrium). In contrast, with velocity-dependent forces breaking the microscopic reversibility, we prove that the detailed balance and the fluctuationdissipation relation mutually exclude each other and no equivalence relation is possible between any two of the three properties. This implies that a steady state of Langevin systems with velocitydependent forces may maintain some equilibrium properties but not all of them. Our results are illustrated with a few example systems.
New trends in nonequilibrium statistical mechanics: classical and quantum systems
Journal of Statistical Mechanics: Theory and Experiment, 2020
The nonlinear relaxation process in many condensed matter systems proceeds through metastable states, giving rise to long-lived states. Stochastic manybody systems, classical and quantum, often display a complex and slow relaxation towards a stationary state. A common phenomenon in the dynamics of out of equilibrium systems is the metastability, and the problem of the lifetime of metastable states involves fundamental aspects of nonequilibrium statistical mechanics. In spite of such ubiquity, the microscopic understanding of metastability and related out of equilibrium dynamics still raise fundamental questions. The aim of this meeting is to bring together scientists interested in the challenging problems connected with dynamics of out of equilibrium classical and quantum physical systems from both theoretical and experimental point of view, within an interdisciplinary context. Specifically, three main areas of outof-equilibrium statistical mechanics will be covered: long range interactions and multistability, anomalous diffusion, and quantum systems. Moreover, the conference will be a discussion forum to promote new ideas in this fertile research field, and in particular new trends such as quantum thermodynamics and novel types of quantum phase transitions occurring in non-equilibrium steady states, and topological phase transitions.
PHYSICAL REVIEW RESEARCH 4, 043125 (2022), 2022
We construct a unified theory of thermodynamics and stochastic thermodynamics for classical nonequilibrium systems driven by non-conservative forces, using the recently developed covariant Ito-Langevin theory. The thermodynamic forces are split into a conservative part and a non-conservative part. Thermodynamic functions are defined using the reference conservative system. Work and heat are partitioned into excess parts and house-keeping parts, which are due to, respectively, conservative forces and non-conservative forces. Excess entropy production (EP) and house-keeping EP are analogously defined. The splitting of thermodynamic forces is subjected to an arbitrariness resembling a gauge symmetry, with each gauge defining a reference conservative Langevin system. In the special Gibbs gauge, the nonequilibrium steady state (NESS) is characterized by Gibbs canonical distribution, the excess heat agrees with that defined by Hatano and Sasa, and the excess EP agrees with that of Glansdorff and Prigogine, i.e., it is the time rate of the second-order variation of system entropy near the NESS. Adopting the Gibbs gauge, and focusing on the excess parts of thermodynamic quantities, a complete analogy between thermodynamics of non-conservative systems and that of conservative systems is established. One important consequence of this analogy is that both the free energy and excess EP are minimized at NESS. Our theory therefore constitutes a statistical foundation both for the steady-state thermodynamics theory due to Sasa and Tasaki and for the stability theory of NESS due to Glansdorff and Prigogine. These results are valid even if the system is far from equilibrium. By studying detailed fluctuation theorem, we find striking differences between systems with symmetric kinetic matrices and those with asymmetric kinetic matrices. For systems with asymmetric kinetic matrices, the total EP is the sum of house-keeping EP, excess EP, and pumped entropy. Entropy pumping is an exchange of entropy between the system and environment without necessarily involving dissipation. In the presence of entropy pumping, the system may behave as either a demon or an antidemon. Fluctuation theorems and work relations are derived both for total work and for excess work. For systems with symmetric kinetic matrices, there is no entropy pumping, yet in the Gibbs gauge, the excess work and house-keeping work each satisfies a separate fluctuation theorem. We illustrate our theory using many concrete examples.
Consistent thermodynamic framework for interacting particles by neglecting thermal noise
Physical Review E, 2015
An effective temperature θ, conjugated to a generalized entropy s q , was introduced recently for a system of interacting particles. Since θ presents values much higher than those of typical room temperatures T θ, the thermal noise can be neglected (T /θ 0) in these systems. Moreover, the consistency of this definition, as well as of a form analogous to the first law of thermodynamics, du = θds q + δW , were verified lately by means of a Carnot cycle, whose efficiency was shown to present the usual form, η = 1 − (θ 2 /θ 1). Herein we explore further the heat contribution δQ = θds q by proposing a way for a heat exchange between two such systems, as well as its associated thermal equilibrium. As a consequence, the zeroth principle is also established. Moreover, we consolidate the first-law proposal by following the usual procedure for obtaining different potentials, i.e., applying Legendre transformations for distinct pairs of independent variables. From these potentials we derive the equation of state, Maxwell relations, and define response functions. All results presented are shown to be consistent with those of standard thermodynamics for T > 0.
Stochastic thermodynamics of active Brownian particles
Physical Review E, 2013
Examples of self propulsion in strongly fluctuating environment is abound in nature, e.g., molecular motors and pumps operating in living cells. Starting from Langevin equation of motion, we develop a stochastic thermodynamic description of non-interacting self propelled particles using simple models of velocity dependent forces. We derive fluctuation theorems for entropy production and a modified fluctuation dissipation relation, characterizing the linear response at non-equilibrium steady states. We study these notions in a simple model of molecular motors, and in the Rayleigh-Helmholtz and energy-depot model of self propelled particles.
Stochastic mechanics of nonequilibrium systems
Brazilian Journal of Physics, 1997
A nonequilibrium system of classical particles interacting through nonconservative forces is studied by a stochastic Markovian process de ned over the space of the particle positions. The velocities of the particles are treated as independent stochocastic variables with a given probability distribution. We deduce expressions for the rate in which energy is exchanged with the surrounding as well as the rate in which energy is dissipated. These results are applied to the special case in which the irrotational and solenoidal parts of the forces acting on the particles are orthogonal. We also solve exactly a model in which these two forces are linear functions of positions.
Nonequilibrium statistical mechanics of open classical systems
XIVth International Congress on Mathematical Physics, 2006
We describe the ergodic and thermodynamical properties of chains of anharmonic oscillators coupled, at the boundaries, to heat reservoirs at positive and different temperatures. We discuss existence and uniqueness of stationary states, rate of convergence to stationarity, heat flows and entropy production, Kubo formula and Gallavotti-Cohen fluctuation theorem.
Microscopic non-equilibrium structure and dynamical model of entropy flow
Foundations of Physics, 1997
The extension of" quantum mechanics to a general functional space ("rigged Hilbert space"), which iru:orporates time-symmetry breaking, is applied to construct exact dynamical models of entropy production arm entropy flow. They are illustrated by using a simple conservative Harni[tonian system j(~r multilevel atoms coupled to a time-dependent e.rternal ./brce. The external jbrce destroys the monotoni~qty of' the ~-Jhnction evolution. This leads to a model of the entropy flow that allows a steady nonequilibrium structure of the emitted field around the unstable particles: