Extreme Current Fluctuations in Lattice Gases: Beyond Nonequilibrium Steady States

TL;DR

This paper uses macroscopic fluctuation theory to classify and analyze large current fluctuations in diffusive lattice gases, revealing two universality classes with distinct behaviors and exact solutions in some cases.

Contribution

It introduces a classification of current fluctuations into elliptic and hyperbolic universality classes based on effective fluid compressibility, extending understanding beyond steady states.

Findings

Identified elliptic and hyperbolic classes of fluctuations.

Derived exact solutions for the Symmetric Simple Exclusion Process.

Conjectured super-Gaussian statistics for certain initial conditions.

Abstract

We use the macroscopic fluctuation theory (MFT) to study large current fluctuations in non-stationary diffusive lattice gases. We identify two universality classes of these fluctuations which we call elliptic and hyperbolic. They emerge in the limit when the deterministic mass flux is small compared to the mass flux due to the shot noise. The two classes are determined by the sign of compressibility of \emph{effective fluid}, obtained by mapping the MFT into an inviscid hydrodynamics. An example of the elliptic class is the Symmetric Simple Exclusion Process where, for some initial conditions, we can solve the effective hydrodynamics exactly. This leads to a super-Gaussian extreme current statistics conjectured by Derrida and Gerschenfeld (2009) and yields the optimal path of the system. For models of the hyperbolic class the deterministic mass flux cannot be neglected, leading to a different extreme current statistics.