Matrix Ansatz for the Fluctuations of the Current in the ASEP with Open Boundaries

TL;DR

This paper develops a matrix product Ansatz to exactly analyze current fluctuations in the ASEP with open boundaries, providing insights into non-equilibrium steady states and their probabilistic properties.

Contribution

It introduces a novel matrix product approach to compute current fluctuation statistics in finite ASEP systems, extending to periodic cases and spin chain models.

Findings

Exact current fluctuation distributions derived

Probabilities of conditioned configurations obtained

Applicability to both open and periodic ASEP demonstrated

Abstract

The Asymmetric Simple Exclusion Process is one of the most extensively studied models in non-equilibrium statistical mechanics. The macroscopic particle current produced in its steady state is directly related to the breaking of detailed balance, and is therefore a physical quantity of particular interest. In this paper, we build a matrix product Ansatz which allows to access the exact statistics of the fluctuations of that current for finite sizes, as well as the probabilities of configurations conditioned on the mean current. We also show how this Ansatz can be used for the periodic ASEP, and how it translates in the language of the XXZ spin chain.