The Fluctuation Theorem as a Gibbs Property

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.