Large deviations for out of equilibrium correlations in the symmetric simple exclusion process

TL;DR

This paper extends large deviation theory to non-equilibrium systems, specifically analyzing the symmetric simple exclusion process, by focusing on two-point correlations and constructing invariant measure approximations.

Contribution

It develops a method to analyze large deviations of two-point correlations in non-equilibrium exclusion processes using invariant measure approximations.

Findings

Derived bounds for large deviations of two-point correlations.

Constructed a quantitative approximation to the invariant measure.

Extended Donsker-Varadhan theory to non-equilibrium settings.

Abstract

For finite size Markov chains, the Donsker-Varadhan theory fully describes the large deviations of the time averaged empirical measure. We are interested in the extension of the Donsker-Varadhan theory for a large size non-equilibrium system: the one-dimensional symmetric simple exclusion process connected with reservoirs at different densities. The Donsker-Varadhan functional encodes a variety of scales depending on the observable of interest. In this paper, we focus on the time-averaged two point correlations and investigate the large deviations from the steady state behaviour. To control two point correlations out of equilibrium, the key input is the construction of a simple approximation to the invariant measure. This approximation is quantitative in time and space as estimated through relative entropy bounds building on the work of Jara and Menezes arXiv:1810.09526.