Factorised Steady States in Mass Transport Models

TL;DR

This paper investigates a class of mass transport models on a one-dimensional periodic lattice, deriving a simple condition for when their steady states can be factorized, covering various models like zero-range and asymmetric processes.

Contribution

It provides a unified, simple criterion for the factorization of steady states in diverse mass transport models, including both discrete and continuous cases.

Findings

Derived a necessary and sufficient condition for steady state factorization.

Unified framework encompassing zero-range and asymmetric random average processes.

Applicable to models with both parallel and sequential dynamics.

Abstract

We study a class of mass transport models where mass is transported in a preferred direction around a one-dimensional periodic lattice and is globally conserved. The model encompasses both discrete and continuous masses and parallel and random sequential dynamics and includes models such as the Zero-range process and Asymmetric random average process as special cases. We derive a necessary and sufficient condition for the steady state to factorise, which takes a rather simple form.