Current Fluctuations in One Dimensional Diffusive Systems with a Step Initial Density Profile

TL;DR

This paper applies macroscopic fluctuation theory to analyze current fluctuations in one-dimensional diffusive systems with a step initial density, revealing symmetry properties and non-Gaussian decay behaviors.

Contribution

It extends MFT to systems with step initial conditions, distinguishes between annealed and quenched averages, and derives current distribution results for various models.

Findings

Current distribution exhibits a symmetry similar to the fluctuation theorem.

Non-Gaussian decay of current distribution is universal in the diffusive regime.

Solutions for non-interacting particles provide insights for other models.

Abstract

We show how to apply the macroscopic fluctuation theory (MFT) of Bertini, De Sole, Gabrielli, Jona-Lasinio, and Landim to study the current fluctuations of diffusive systems with a step initial condition. We argue that one has to distinguish between two ways of averaging (the annealed and the quenched cases) depending on whether we let the initial condition fluctuate or not. Although the initial condition is not a steady state, the distribution of the current satisfies a symmetry very reminiscent of the fluctuation theorem. We show how the equations of the MFT can be solved in the case of non-interacting particles. The symmetry of these equations can be used to deduce the distribution of the current for several other models, from its knowledge for the symmetric simple exclusion process. In the range where the integrated current $Q_t \sim \sqrt{t}$, we show that the non-Gaussian decay $\exp [- Q_t^3/t]$ of the distribution of $Q_t$ is generic.