Large deviations of lattice Hamiltonian dynamics coupled to stochastic thermostats

TL;DR

This paper develops a theoretical framework for analyzing large deviations in lattice Hamiltonian systems with stochastic thermostats, deriving formulas for the large deviation functional and exploring stationary states and current fluctuations.

Contribution

It introduces a general formula for the Donsker-Varadhan large deviation functional in Hamiltonian systems with stochastic thermostats and connects stationary states to a variational principle.

Findings

Derived a formula for the large deviation functional under time-reversal symmetry.

Characterized the stationary state via a variational principle related to entropy production.

Computed the large deviation functional of the current for a harmonic chain with stochastic coupling.

Abstract

We discuss the Donsker-Varadhan theory of large deviations in the framework of Hamiltonian systems thermostated by a Gaussian stochastic coupling. We derive a general formula for the Donsker-Varadhan large deviation functional for dynamics which satisfy natural properties under time reversal. Next, we discuss the characterization of the stationary state as the solution of a variational principle and its relation to the minimum entropy production principle. Finally, we compute the large deviation functional of the current in the case of a harmonic chain thermostated by a Gaussian stochastic coupling.