On the Application of the Gallavotti-Cohen Fluctuation Relation to Thermostatted Steady States Near Equilibrium

TL;DR

This paper investigates the applicability of the Gallavotti-Cohen Fluctuation Relation to thermostatted steady states near equilibrium, finding it does not generally hold for such systems, but related dissipation function relations do.

Contribution

The study analyzes non-Anosov, realistic steady state systems and shows the GCFT fluctuation relation does not apply near equilibrium, unlike related dissipation function relations.

Findings

GCFT fluctuation relation does not hold near equilibrium for these systems.

Dissipation function fluctuation relations are valid both near and far from equilibrium.

Discrepancies in fluctuation relations decrease as systems move away from equilibrium.

Abstract

The fluctuation relation of the Gallavotti-Cohen Fluctuation Theorem (GCFT) concerns fluctuations in the phase space compression rate of dissipative, reversible dynamical systems. It has been proven for Anosov systems, but it is expected to apply more generally. This raises the question of which non-Anosov systems satisfy the fluctuation relation. We analyze time dependent fluctuations in the phase space compression rate of a class of N-particle systems that are at equilibrium or in near equilibrium steady states. This class does not include Anosov systems or isoenergetic systems, however, it includes most steady state systems considered in molecular dynamics simulations of realistic systems. We argue that the fluctuations of the phase space compression rate of these systems at or near equilibrium do not satisfy the fluctuation relation of the GCFT, although the discrepancies become somewhat smaller as the systems move further from equilibrium. In contrast, similar fluctuation relations for an appropriately defined dissipation function appear to hold both near and far from equilibrium.