Work relation in non-equilibrium steady states of one-dimensional quantum lattice systems

Abstract

We consider the non-equilibrium steady state induced by two infinitely extended quantum thermal reservoirs at different inverse temperatures β + Δβ, β − Δβ and derive a work relation. We consider global cyclic operations and derive an upper bound of the work density in one-dimensional quantum lattice systems. This relation reproduces the second law of thermodynamics in the equilibrium limit Δβ → 0. A free fermion system is discussed as an example, and the physical interpretation is given to the upper bound.