Landau Theory for Non-Equilibrium Steady States

TL;DR

This paper extends Landau theory to non-equilibrium steady states near phase transitions, accounting for non-analytic potentials arising from multiple baths or driving, and explores critical exponents beyond mean-field approximation.

Contribution

It introduces a Landau framework for non-equilibrium steady states with non-analytic potentials and analyzes the impact of bath properties on critical behavior.

Findings

Non-analytic Landau potentials describe non-equilibrium steady states.

Multiple baths induce non-analyticities in the potential.

Critical exponents depend on bath singularities.

Abstract

We examine how systems in non-equilibrium steady states close to a continuous phase transition can still be described by a Landau potential if one forgoes the assumption of analyticity. In a system simultaneously coupled to several baths at different temperatures, the non-analytic potential arises from the different density of states of the baths. In periodically driven-dissipative systems, the role of multiple baths is played by a single bath transferring energy at different harmonics of the driving frequency. The mean-field critical exponents become dependent on the low-energy features of the two most singular baths. We propose an extension beyond mean field.