The Steady State Fluctuation Relation for the Dissipation Function

TL;DR

This paper proves a general transient fluctuation relation for entropy production in reversible systems and discusses conditions under which it leads to a robust steady state fluctuation relation, highlighting its broad applicability.

Contribution

It provides a general proof of the steady state fluctuation relation for the dissipation function in nonequilibrium systems, emphasizing its robustness and broad conditions.

Findings

Transient fluctuation relation holds for most time reversible dynamics.

Steady state fluctuation relation can be derived from transient relations under certain conditions.

The steady state relation is robust and similar to equilibrium thermodynamic equalities.

Abstract

We give a proof of transient fluctuation relations for the entropy production (dissipation function) in nonequilibrium systems, which is valid for most time reversible dynamics. We then consider the conditions under which a transient fluctuation relation yields a steady state fluctuation relation for driven nonequilibrium systems whose transients relax, producing a unique nonequilibrium steady state. Although the necessary and sufficient conditions for the production of a unique nonequilibrium steady state are unknown, if such a steady state exists, the generation of the steady state fluctuation relation from the transient relation is shown to be very general. It is essentially a consequence of time reversibility and of a form of decay of correlations in the dissipation, which is needed also for, e.g., the existence of transport coefficients. Because of this generality the resulting steady state fluctuation relation has the same degree of robustness as do equilibrium thermodynamic equalities. The steady state fluctuation relation for the dissipation stands in contrast with the one for the phase space compression factor, whose convergence is problematic, for systems close to equilibrium. We examine some model dynamics that have been considered previously, and show how they are described in the context of this work.