An Exact Formula for the Statistics of the Current in the TASEP with Open Boundaries

TL;DR

This paper derives an exact, parametric formula for the generating function of the current's cumulants in the TASEP with open boundaries, applicable to all system sizes and boundary conditions.

Contribution

It provides a universal, exact formula for the current statistics in the TASEP with open boundaries, extending previous approximate or limited results.

Findings

Exact formula for the generating function of current cumulants

Applicable to all system sizes and boundary parameters

Links to large deviation function via Laplace transform

Abstract

We study the totally asymmetric exclusion process (TASEP) on a finite one-dimensional lattice with open boundaries, i.e., in contact with two reservoirs at different potentials. The total (time-integrated) current through the system is a random variable that scales linearly with time in the long time limit. We give a parametric representation for the generating function of the cumulants of the current, which is related to the large deviation function by Laplace transform. This formula is valid for all system sizes and for all values of the boundary coupling parameters.