Factorised steady states for multi-species mass transfer models

TL;DR

This paper derives conditions under which multi-species mass transfer models on lattices have factorised steady states, providing explicit results for various update rules and lattice structures.

Contribution

It introduces necessary and sufficient conditions for steady state factorisation in multi-species mass transfer models, generalising to arbitrary lattices and different update schemes.

Findings

Derived conditions for factorisation in one-dimensional models

Extended results to arbitrary lattice structures

Provided explicit solutions for different update rules

Abstract

A general class of mass transport models with Q species of conserved mass is considered. The models are defined on a lattice with parallel discrete time update rules. For one-dimensional, totally asymmetric dynamics we derive necessary and sufficient conditions on the mass transfer dynamics under which the steady state factorises. We generalise the model to mass transfer on arbitrary lattices and present sufficient conditions for factorisation. In both cases, explicit results for random sequential update and continuous time limits are given.