Lee-Yang zeros and phase transitions in nonequilibrium steady states

TL;DR

This paper extends the Lee-Yang theory of phase transitions to nonequilibrium steady states by analyzing zeros of the normalization factor in a specific model, revealing patterns similar to equilibrium phase transitions.

Contribution

It introduces a method to study phase transitions in nonequilibrium systems using zeros of the steady-state normalization factor, with exact results for a boundary-driven exclusion process.

Findings

Zeros distribution follows Lee-Yang patterns at phase transitions

Exact zeros distribution obtained in the thermodynamic limit

First and second order transitions exhibit known Lee-Yang zero patterns

Abstract

We consider how the Lee-Yang description of phase transitions in terms of partition function zeros applies to nonequilibrium systems. Here one does not have a partition function, instead we consider the zeros of a steady-state normalization factor in the complex plane of the transition rates. We obtain the exact distribution of zeros in the thermodynamic limit for a specific model, the boundary-driven asymmetric simple exclusion process. We show that the distributions of zeros at the first and second order nonequilibrium phase transitions of this model follow the patterns known in the Lee-Yang equilibrium theory.