Anomalous current fluctuations from Euler hydrodynamics

TL;DR

This paper investigates the origin of unusual current fluctuations in stochastic cellular automata using hydrodynamic theory, revealing how initial fluctuations evolve and characterizing their probability distributions through analytical and numerical methods.

Contribution

It introduces a hydrodynamic framework to explain anomalous current fluctuations in stochastic automata, connecting microscopic results with macroscopic fluctuation theory.

Findings

Initial fluctuations propagated by Euler equations explain both typical and large fluctuations.

An additional contribution affects typical fluctuations in stochastic dynamics.

Numerical simulations confirm the conjectured probability distribution for fluctuations.

Abstract

We consider the hydrodynamic origin of anomalous current fluctuations in a family of stochastic charged cellular automata. Using ballistic macroscopic fluctuation theory, we study both typical and large fluctuations of the charge current and reproduce microscopic results which are available for the deterministic single-file limit of the models. Our results indicate that in general initial fluctuations propagated by Euler equations fully characterize both scales of anomalous fluctuations. For stochastic dynamics, we find an additional contribution to typical fluctuations and conjecture the functional form of the typical probability distribution, which we confirm by numerical simulations.