A perturbative approach to the macroscopic fluctuation theory

TL;DR

This paper develops a perturbative method within macroscopic fluctuation theory to analyze stationary states of diffusive systems out of equilibrium, revealing non-zero long-range correlations at first order in small forcing.

Contribution

It introduces a perturbative approach to compute the large deviation functional for density in non-equilibrium diffusive systems with arbitrary transport coefficients.

Findings

Long-range correlations are generally non-zero in non-equilibrium steady states.

The method applies to general domains in  and arbitrary diffusive dynamics.

It extends previous exactly solvable models by analyzing more general cases.

Abstract

In this paper, we study the stationary states of diffusive dynamics driven out of equilibrium by reservoirs. For a small forcing, the system remains close to equilibrium and the large deviation functional of the density can be computed perturbatively by using the macroscopic fluctuation theory. This applies to general domains in $\mathbb{R}^d$ and diffusive dynamics with arbitrary transport coefficients. As a consequence, one can analyse the correlations at the first non trivial order in the forcing and show that, in general, all the long range correlation functions are not equal to 0, in contrast to the exactly solvable models previously known.