The Fluctuation Theorem as a Gibbs Property

TL;DR

This paper interprets the Gallavotti-Cohen fluctuation theorem within the Gibbs formalism, establishing it as a property of Gibbs measures and extending it to certain stochastic dynamics.

Contribution

It demonstrates that the fluctuation theorem can be understood as a Gibbs property and provides a local version applicable to spatially extended stochastic systems.

Findings

Fluctuation theorem is a Gibbs property derived from Gibbs state definitions.

A local version of the fluctuation theorem is formulated within the Gibbsian framework.

Extension of the fluctuation theorem to some spatially extended stochastic dynamics.

Abstract

Common ground to recent studies exploiting relations between dynamical systems and non-equilibrium statistical mechanics is, so we argue, the standard Gibbs formalism applied on the level of space-time histories. The assumptions (chaoticity principle) underlying the Gallavotti-Cohen fluctuation theorem make it possible, using symbolic dynamics, to employ the theory of one-dimensional lattice spin systems. The Kurchan and Lebowitz-Spohn analysis of this fluctuation theorem for stochastic dynamics can be restated on the level of the space-time measure which is a Gibbs measure for an interaction determined by the transition probabilities. In this note we understand the fluctuation theorem as a Gibbs property as it follows from the very definition of Gibbs state. We give a local version of the fluctuation theorem in the Gibbsian context and we derive from this a version also for some class of spatially extended stochastic dynamics.