Exact joint density-current probability function for the asymmetric exclusion process

TL;DR

This paper derives the exact joint probability function for occupation number and current in the asymmetric exclusion process with open boundaries, revealing non-Gaussian distributions and phase transition effects.

Contribution

It introduces a novel operator algebra approach to obtain the exact joint density-current distribution for the asymmetric exclusion process.

Findings

Density fluctuations are discontinuous at the phase transition.

Current fluctuations remain continuous across the phase transition.

Distribution is non-Gaussian in the thermodynamic limit.

Abstract

We study the asymmetric exclusion process with open boundaries and derive the exact form of the joint probability function for the occupation number and the current through the system. We further consider the thermodynamic limit, showing that the resulting distribution is non-Gaussian and that the density fluctuations have a discontinuity at the continuous phase transition, while the current fluctuations are continuous. The derivations are performed by using the standard operator algebraic approach, and by the introduction of new operators satisfying a modified version of the original algebra.