Fluctuation Relation beyond Linear Response Theory

TL;DR

This paper develops a theory for finite time corrections to the Fluctuation Relation (FR), enabling better comparison between theoretical predictions and numerical observations in nonequilibrium systems, especially where non-Gaussian fluctuations occur.

Contribution

The paper introduces a finite time correction theory for FR and validates it through numerical tests in non-Gaussian fluctuation regimes, extending the applicability of FR beyond linear response.

Findings

Finite time corrections improve FR predictions in numerical simulations.

FR is verified in non-Gaussian fluctuation regimes independent of linear response.

Neglecting finite time corrections could lead to apparent violations of FR.

Abstract

The Fluctuation Relation (FR) is an asymptotic result on the distribution of certain observables averaged over time intervals T as T goes to infinity and it is a generalization of the fluctuation--dissipation theorem to far from equilibrium systems in a steady state which reduces to the usual Green-Kubo (GK) relation in the limit of small external non conservative forces. FR is a theorem for smooth uniformly hyperbolic systems, and it is assumed to be true in all dissipative ``chaotic enough'' systems in a steady state. In this paper we develop a theory of finite time corrections to FR, needed to compare the asymptotic prediction of FR with numerical observations, which necessarily involve fluctuations of observables averaged over finite time intervals T. We perform a numerical test of FR in two cases in which non Gaussian fluctuations are observable while GK does not apply and we get a non trivial verification of FR that is independent of and different from linear response theory. Our results are compatible with the theory of finite time corrections to FR, while FR would be observably violated, well within the precision of our experiments, if such corrections were neglected.