Mapping Nonequilibrium onto Equilibrium: The Macroscopic Fluctuations of Simple Transport Models

TL;DR

This paper demonstrates a nonlocal transformation that maps the large deviations of a boundary-driven transport model to an equilibrium-like system, enabling explicit solutions for fluctuation probabilities.

Contribution

It introduces a novel nonlocal mapping that relates nonequilibrium fluctuations to equilibrium systems, facilitating analytical solutions for large deviations.

Findings

Mapping simplifies the calculation of large deviations

The approach generalizes to other models with macroscopic fluctuation theory

Explicit large-deviation functions can be obtained through elementary transformations

Abstract

We study a simple transport model driven out of equilibrium by reservoirs at the boundaries, corresponding to the hydrodynamic limit of the symmetric simple exclusion process. We show that a nonlocal transformation of densities and currents maps the large deviations of the model into those of an open, isolated chain satisfying detailed balance, where rare fluctuations are the time reversals of relaxations. We argue that the existence of such a mapping is the immediate reason why it is possible for this model to obtain an explicit solution for the large-deviation function of densities through elementary changes of variables. This approach can be generalized to the other models previously treated with the macroscopic fluctuation theory.