Non-zero entropy density in the XY chain out of equilibrium

TL;DR

This paper proves that the von Neumann entropy density remains non-zero in the non-equilibrium steady state of the XY chain, and it exceeds the thermal equilibrium density, highlighting persistent quantum disorder.

Contribution

It demonstrates that the entropy density in the XY chain out of equilibrium is strictly positive and greater than in thermal equilibrium, providing new insights into quantum non-equilibrium states.

Findings

Entropy density is non-zero for large blocks in non-equilibrium steady states.

Non-equilibrium density exceeds thermal equilibrium density.

Results apply to XY chain coupled to thermal reservoirs at different temperatures.

Abstract

The von Neumann entropy density of a block of n spins is proved to be non-zero for large n in the non-equilibrium steady state of the XY chain constructed by coupling a finite cutout of the chain to the two infinite parts to its left and right which act as thermal reservoirs at different temperatures. Moreover, the non-equilibrium density is shown to be strictly greater than the density in thermal equilibrium.