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

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.