Macroscopic current fluctuations in stochastic lattice gases

TL;DR

This paper extends the dynamic approach to analyze macroscopic current fluctuations in stochastic lattice gases, deriving large deviation estimates and generalizing previous results with explicit model examples.

Contribution

It introduces a generalized framework for large deviation estimates of current fluctuations in lattice gases, expanding upon prior models and including explicit examples.

Findings

Derived large deviation estimates for current fluctuations

Generalized previous results to broader models

Provided explicit examples illustrating the theory

Abstract

We study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach to density fluctuations developed in previous articles. More precisely, we derive large deviation estimates for the space--time fluctuations of the empirical current which include the previous results. Large time asymptotic estimates for the fluctuations of the time average of the current, recently established by Bodineau and Derrida, can be derived in a more general setting. There are models where we have to modify their estimates and some explicit examples are introduced.