Computation of current cumulants for small nonequilibrium systems

TL;DR

This paper presents a systematic algorithm for exactly computing current cumulants in small nonequilibrium systems, extending full counting statistics methods and applying them to boundary-driven Kawasaki dynamics.

Contribution

It introduces a path-distribution identity-based method for calculating current cumulants and extends it to joint statistics of multiple currents, with thermodynamical interpretation.

Findings

Effective computation of current cumulants in boundary-driven Kawasaki dynamics.

Extension of the method to multiple current statistics.

Comparison with Onsager-Machlup formalism for thermodynamical insights.

Abstract

We analyze a systematic algorithm for the exact computation of the current cumulants in stochastic nonequilibrium systems, recently discussed in the framework of full counting statistics for mesoscopic systems. This method is based on identifying the current cumulants from a Rayleigh-Schrodinger perturbation expansion for the generating function. Here it is derived from a simple path-distribution identity and extended to the joint statistics of multiple currents. For a possible thermodynamical interpretation, we compare this approach to a generalized Onsager-Machlup formalism. We present calculations for a boundary driven Kawasaki dynamics on a one-dimensional chain, both for attractive and repulsive particle interactions.