Non equilibrium steady states: fluctuations and large deviations of the density and of the current

TL;DR

This paper reviews methods like the matrix ansatz, additivity principle, and macroscopic fluctuation theory to analyze fluctuations and large deviations of density and current in non-equilibrium steady states, especially in exclusion processes.

Contribution

It introduces and compares recent theoretical methods for calculating fluctuations and large deviations in non-equilibrium steady states, highlighting their differences from equilibrium systems.

Findings

Methods enable calculation of non-Gaussian fluctuations.

Large deviation functions can be non-convex.

Properties differ significantly from equilibrium cases.

Abstract

These lecture notes give a short review of methods such as the matrix ansatz, the additivity principle or the macroscopic fluctuation theory, developed recently in the theory of non-equilibrium phenomena. They show how these methods allow to calculate the fluctuations and large deviations of the density and of the current in non-equilibrium steady states of systems like exclusion processes. The properties of these fluctuations and large deviation functions in non-equilibrium steady states (for example non-Gaussian fluctuations of density or non-convexity of the large deviation function which generalizes the notion of free energy) are compared with those of systems at equilibrium.