From the microscopic to the van Hove regime in the XY chain out of equilibrium

TL;DR

This paper rigorously constructs and analyzes the nonequilibrium steady state in the XY chain, demonstrating that the van Hove weak coupling regime accurately captures the leading entropy production behavior.

Contribution

It provides a rigorous mathematical construction of the nonequilibrium steady state in the XY chain and links the microscopic entropy production to the van Hove regime.

Findings

The steady state is thermodynamically nontrivial.

The van Hove regime reproduces the leading entropy production.

The microscopic and van Hove regimes are connected in the XY chain.

Abstract

Using the framework of rigorous algebraic quantum statistical mechanics, we construct the unique nonequilibrium steady state in the isotropic XY chain in which a sample of arbitrary finite size is coupled by a bond coupling perturbation of arbitrary strength to two infinitely extended thermal reservoirs, and we prove that this state is thermodynamically nontrivial. Moreover, extracting the leading second order contribution to its microscopic entropy production and deriving its entropy production in the van Hove weak coupling regime, we prove that, in the mathematically and physically important XY chain, the van Hove regime reproduces the leading order contribution to the microscopic regime.