Fluctuations of Current in Non-Stationary Diffusive Lattice Gases

TL;DR

This paper uses macroscopic fluctuation theory to analyze current fluctuations in one-dimensional diffusive lattice gases with step-like initial conditions, providing analytical variance formulas and numerical large deviation results.

Contribution

It introduces a perturbative approach to compute current fluctuation variances for a broad class of diffusive processes with arbitrary initial conditions.

Findings

Analytical variance formulas for current fluctuations in diffusive lattice gases.

Numerical analysis of large deviations for the symmetric exclusion process.

Application of theory to models like symmetric exclusion and Kipnis-Marchioro-Presutti.

Abstract

We employ the macroscopic fluctuation theory to study fluctuations of integrated current in one-dimensional lattice gases with a step-like initial density profile. We analytically determine the variance of the current fluctuations for a class of diffusive processes with a density-independent diffusion coefficient, but otherwise arbitrary. Our calculations rely on a perturbation theory around the noiseless hydrodynamic solution. We consider both quenched and annealed types of averaging (the initial condition is allowed to fluctuate in the latter situation). The general results for the variance are specialized to a few interesting models including the symmetric exclusion process and the Kipnis-Marchioro-Presutti model. We also probe large deviations of the current for the symmetric exclusion process. This is done by numerically solving the governing equations of the macroscopic fluctuation theory using an efficient iteration algorithm.