Monotone return to steady nonequilibrium (original) (raw)

Monotonic Return to Steady Nonequilibrium

Physical Review Letters, 2011

We propose and analyze a new candidate Lyapunov function for relaxation towards general nonequilibrium steady states. The proposed functional is obtained from the large time asymptotics of time-symmetric fluctuations. For driven Markov jump or diffusion processes it measures an excess in dynamical activity rates. We present numerical evidence and we report on a rigorous argument for its monotonous time-dependence close to the steady nonequilibrium or in general after a long enough time. This is in contrast with the behavior of approximate Lyapunov functions based on entropy production that when driven far from equilibrium often keep exhibiting temporal oscillations even close to stationarity.

Nonequilibrium linear response for Markov dynamics, I: Jump processes and overdamped diffusions

Journal of Statistical Physics, 2009

Systems out of equilibrium, in stationary as well as in nonstationary regimes, display a linear response to energy impulses simply expressed as the sum of two specific temporal correlation functions. There is a natural interpretation of these quantities. The first term corresponds to the correlation between observable and excess entropy flux yielding a relation with energy dissipation like in equilibrium. The second term comes with a new meaning: it is the correlation between the observable and the excess in dynamical activity or reactivity, playing an important role in dynamical fluctuation theory out-of-equilibrium. It appears as a generalized escape rate in the occupation statistics. The resulting response formula holds for all observables and allows direct numerical or experimental evaluation, for example in the discussion of effective temperatures, as it only involves the statistical averaging of explicit quantities, e.g. without needing an expression for the nonequilibrium distribution. The physical interpretation and the mathematical derivation are independent of many details of the dynamics, but in this first part they are restricted to Markov jump processes and overdamped diffusions.

Monotonicity of the dynamical activity

We find a new Lyapunov function for the time-evolution of probability distributions evolving under a Master equation, possibly relevant for the characterization of steady nonequilibria. This function is non-entropic when the system is driven away from detailed balance; it rather measures an excess in dynamical activity. Our proof of monotone behavior works under two conditions: (1) the initial distribution is close enough to stationarity, or equivalently for our context, we look at large times, and

Fluctuations in Stationary Nonequilibrium States of Irreversible Processes

Physical Review Letters, 2001

In this paper we formulate a dynamical fluctuation theory for stationary non equilibrium states (SNS) which covers situations in a nonlinear hydrodynamic regime and is verified explicitly in stochastic models of interacting particles. In our theory a crucial role is played by the time reversed dynamics. Our results include the modification of the Onsager-Machlup theory in the SNS, a general Hamilton-Jacobi equation for the macroscopic entropy and a non equilibrium, non linear fluctuation dissipation relation valid for a wide class of systems. PACS numbers: 05.20.-y, 05.40.-a, 05.60.-k

On and beyond entropy production: the case of Markov jump processes

Arxiv preprint arXiv:0709.4327, 2007

Abstract: How is it that entropy derivatives almost in their own are characterizing the state of a system close to equilibrium, and what happens further away from it? We explain within the framework of Markov jump processes why fluctuation theory can be based on ...

B.: Nonequilibrium linear response for Markov dynamics, I: Jump processes and overdamped diffusions

2009

We continue our study of the linear response of a nonequilibrium system. This Part II concentrates on models of open and driven inertial dynamics but the structure and the interpretation of the result remain unchanged: the response can be expressed as a sum of two temporal correlations in the unperturbed system, one entropic, the other frenetic. The decomposition arises from the (anti)symmetry under time-reversal on the level of the nonequilibrium action. The response formula involves a statistical averaging over explicitly known observables but, in contrast with the equilibrium situation, they depend on the model dynamics in terms of an excess in dynamical activity. As an example, the Einstein relation between mobility and diffusion constant is modified by a correlation term between the position and the momentum of the particle.

Nonequilibrium stochastic processes: Time dependence of entropy flux and entropy production

Physical Review E, 2002

Based on the Fokker-Planck and the entropy balance equations we have studied the relaxation of a dissipative dynamical system driven by external Ornstein-Uhlenbeck noise processes in the absence and presence of nonequilibrium constraint in terms of the thermodynamically inspired quantities such as entropy flux and entropy production. The interplay of nonequilibrium constraint, dissipation, and noise reveals some interesting extremal nature in the time dependence of entropy flux and entropy production.