Non-equilibrium stationary state of a two-temperature spin chain

TL;DR

This paper investigates a one-dimensional Ising model coupled to two heat baths at different temperatures, deriving a perturbative solution for its non-equilibrium steady state and analyzing the emergence of complex spin correlations.

Contribution

It introduces a perturbation expansion approach to solve the master equation for a two-temperature spin chain, revealing new spin operators and non-equilibrium features.

Findings

Explicit first two corrections to equilibrium distribution

Emergence of longer-range spin operators in steady state

Violation of detailed balance and entropy production

Abstract

A kinetic one-dimensional Ising model is coupled to two heat baths, such that spins at even (odd) lattice sites experience a temperature $T_{e}$ ($% T_{o}$). Spin flips occur with Glauber-type rates generalised to the case of two temperatures. Driven by the temperature differential, the spin chain settles into a non-equilibrium steady state which corresponds to the stationary solution of a master equation. We construct a perturbation expansion of this master equation in terms of the temperature difference and compute explicitly the first two corrections to the equilibrium Boltzmann distribution. The key result is the emergence of additional spin operators in the steady state, increasing in spatial range and order of spin products. We comment on the violation of detailed balance and entropy production in the steady state.