Fluctuations of stochastic charged cellular automata

TL;DR

This paper derives exact statistical descriptions of charge fluctuations in a stochastic cellular automaton with propagating vacancies and particles, revealing a distribution that interpolates between known fluctuation regimes.

Contribution

It introduces a novel exactly solvable model linking cellular automata with a colored stochastic six-vertex model, providing new insights into charge fluctuation behaviors.

Findings

Charge current fluctuations follow a one-parameter distribution.

Distribution interpolates between single-file reflection and Gaussian transmission regimes.

Exact full counting statistics are obtained for the model.

Abstract

We obtain the exact full counting statistics of a cellular automaton with freely propagating vacancies and charged particles that are stochastically scattered or transmitted upon collision by identifying the problem as a colored stochastic six-vertex model with one inert color. Typical charge current fluctuation at vanishing net charge follow a one-parameter distribution that interpolates between the distribution of the charged single-file class in the limit of pure reflection and a Gaussian distribution in the limit of pure transmission.