# A mass transport model with a simple non-factorized steady-state distribution

## TL;DR

This paper introduces a mass transport model on a ring with a simple non-factorized steady-state distribution, analyzing its properties and measures of distance from equilibrium.

## Contribution

It presents a new mass transport model with a non-factorized steady-state, explicitly derives the non-equilibrium free energy, and compares various non-equilibrium measures.

## Key findings

- Steady-state distribution is a sum of two inhomogeneous product measures.
- A symmetric redistribution yields a factorized, equilibrium measure.
- Explicit expressions for non-equilibrium free energy and related parameters.

## Abstract

We study a mass transport model on a ring with parallel update, where a continuous mass is randomly redistributed along distinct links of the lattice, choosing at random one of the two partitions at each time step. The redistribution process on a given link depends on the masses on both sites, at variance with the Zero Range Process and its continuous mass generalizations. We show that the steady-state distribution takes a simple non-factorized form that can be written as a sum of two inhomogeneous product measures. A factorized measure is recovered for a symmetric mass redistribution, corresponding to an equilibrium process. A non-equilibrium free energy can be explicitly defined from the partition function. We evaluate different characterizations of the `distance' to equilibrium, either dynamic or static: the mass flux, the entropy production rate, the Gibbs free-energy difference between the equilibrium and non-equilibrium stationary states, and the derivative of the non-equilibrium free energy with respect to the applied driving force. The connection between these different non-equilibrium parameters is discussed.