Energy repartition in the nonequilibrium steady state

TL;DR

This paper introduces a spectral temperature concept for nonequilibrium steady states, demonstrated through analytic solutions of a spin chain, revealing mode-dependent temperatures influenced by external fields and interactions.

Contribution

It proposes a novel energy repartition principle leading to spectral temperature in nonequilibrium systems, with broad applicability beyond spin chains.

Findings

Spectral temperature varies across modes in nonequilibrium steady states.

External magnetic field gradients localize spin waves, affecting energy distribution.

Magnon interactions modify the spectral temperature, indicating renormalization effects.

Abstract

The concept of temperature in nonequilibrium thermodynamics is an outstanding theoretical issue. We propose an energy repartition principle that leads to a spectral (mode-dependent) temperature in steady-state nonequilibrium systems. The general concepts are illustrated by analytic solutions of the classical Heisenberg spin chain connected to Langevin heat reservoirs with arbitrary temperature profiles. Gradients of external magnetic fields are shown to localize spin waves in a Wannier-Zeemann fashion, while magnon interactions renormalize the spectral temperature. Our generic results are applicable to other thermodynamic systems such as Newtonian liquids, elastic solids, and Josephson junctions.