Fluctuation theorems and inequalities generalizing the second law of thermodynamics off equilibrium

TL;DR

This paper develops a comprehensive framework for non-stationary non-equilibrium systems, extending fluctuation theorems and second law inequalities beyond equilibrium conditions, based on a generalized Hatano-Sasa relation.

Contribution

It introduces a new theoretical approach for non-stationary systems, generalizing fluctuation theorems and second law inequalities for systems driven away from equilibrium.

Findings

Detailed fluctuation theorems hold for parts of entropy production.

Generalized second-law inequalities are derived for non-stationary states.

Framework applies to systems driven by time-dependent perturbations.

Abstract

We present a general framework for systems which are prepared in a non-stationary non-equilibrium state in the absence of any perturbation, and which are then further driven through the application of a time-dependent perturbation. We distinguish two different situations depending on the way the non-equilibrium state is prepared, either it is created by some driving; or it results from a relaxation following some initial non-stationary conditions. Our approach is based on a recent generalization of the Hatano-Sasa relation for non-stationary probability distributions. We also investigate whether a form of second law holds for separate parts of the entropy production, in a way similar to the work of M. Esposito et al., Phys. Rev. Lett., 104:090601 (2010), but for a non-stationary reference process instead of a stationary one. We find that although the special structure of the theorems derived in this reference is not recovered in the general case, detailed fluctuation theorems still hold separately for parts of the entropy production in this case. These detailed fluctuation theorems lead to interesting generalizations of the second-law of thermodynamics off equilibrium.