Exact computation of current cumulants in small Markovian systems

TL;DR

This paper presents an algorithm for exact calculation of current cumulants in small Markovian systems, utilizing perturbation expansion, with applications demonstrated through numerical evidence in exclusion processes.

Contribution

The paper introduces a novel perturbation-based algorithm for computing exact current cumulants in Markovian systems, extending to covariances of multiple currents.

Findings

Numerical evidence supports a relation between second and fourth cumulants in symmetric exclusion processes.

The method accurately computes mean, variance, and higher cumulants of current.

The approach can be extended to analyze covariances of multiple currents.

Abstract

We describe an algorithm computing the exact value of the mean current, its variance, and higher order cumulants for stochastic driven systems. The method uses a Rayleigh-Schrodinger perturbation expansion of the generating function of the current, and can be extended to compute covariances of multiple currents. As an example of application of the method, we give numerical evidence for a simple relation [Eq.(5)] between the second and the fourth cumulants of the current in a symmetric exclusion process.