Interacting Non-equilibrium Systems with Two Temperatures

TL;DR

This paper models two interconnected magnetic systems at different temperatures, deriving exact solutions for their magnetizations and revealing complex non-equilibrium phase behavior through a novel analytical approach.

Contribution

It introduces an exactly solvable model for two coupled non-equilibrium systems at different temperatures, extending statistical mechanics methods to analyze their steady states.

Findings

Identification of non-equilibrium phases via fixed points of a nonlinear map

Analysis of phase transitions driven by heat transfer between systems

Exact solutions for magnetizations in a two-temperature non-equilibrium model

Abstract

We investigate a simplified model of two fully connected magnetic systems maintained at different temperatures by virtue of being connected to two independent thermal baths while simultaneously being inter-connected with each other. Using generating functional analysis, commonly used in statistical mechanics, we find exactly soluble expressions for their individual magnetisations that define a two-dimensional non-linear map, the equations of which have the same form as those obtained for densely connected equilibrium systems. Steady states correspond to the fixed points of this map, separating the parameter space into a rich set of non-equilibrium phases that we analyse in asymptotically high and low (non-equilibrium) temperature limits. The theoretical formalism is shown to subvert to the classical non-equilibrium steady state problem for two interacting systems with a non-zero heat transfer between them that catalyses a phase transition between ambient non-equilibrium states.