A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics

TL;DR

This paper generalizes the Gallavotti-Cohen fluctuation theorem to various Markov processes, linking symmetry in large deviation functions to entropy production, and explicitly computes the functional for the asymmetric simple exclusion process.

Contribution

It extends the fluctuation theorem to a broad class of stochastic processes and derives new symmetry relations, including explicit calculations for specific models.

Findings

Established a symmetry property of the large deviation function for general Markov processes.

Linked the fluctuation theorem's action functional to entropy production under local detailed balance.

Explicitly computed the large deviation functional for the asymmetric simple exclusion process using Bethe ansatz.

Abstract

We extend the work of Kurchan on the Gallavotti-Cohen fluctuation theorem, which yields a symmetry property of the large deviation function, to general Markov processes. These include jump processes describing the evolution of stochastic lattice gases driven in the bulk or through particle reservoirs, general diffusive processes in physical and/or velocity space, as well as Hamiltonian systems with stochastic boundary conditions. For dynamics satisfying local detailed balance we establish a link between the action functional of the fluctuation theorem and the entropy production. This gives, in the linear regime, an alternative derivation of the Green-Kubo formula and the Onsager reciprocity relations. In the nonlinear regime consequences of the new symmetry are harder to come by and the large derivation functional difficult to compute. For the asymmetric simple exclusion process the latter is determined explicitly using the Bethe ansatz in the limit of large N.