Non-equilibrium steady states with a spatial Markov structure

TL;DR

This paper characterizes the structure of non-equilibrium steady states with a spatial Markov property in exactly solvable chain models, revealing that under certain conditions, these states align with a Dirichlet process previously identified in harmonic models.

Contribution

It provides a complete characterization of mixture measures with a spatial Markov property in NESS models, linking them to the Dirichlet process.

Findings

Mixture measures in NESS are characterized completely.

Under natural conditions, these measures coincide with the Dirichlet process.

The results generalize previous findings from harmonic models.

Abstract

We investigate the structure of non-equilibrium steady states (NESS) for a class of exactly solvable models in the setting of a chain with left and right reservoirs. Inspired by recent results on the harmonic model, we focus on models in which the NESS is a mixture of equilibrium product measures, and where the probability measure which describes the mixture has a spatial Markovian property. We completely characterize the structure of such mixture measures, and show that under natural scaling and translation invariance properties, the only possible mixture measures are coinciding with the Dirichlet process found earlier in the context of the harmonic model.