The second law-type work relation in non-equilibrium steady states in one-dimensional quantum lattice systems

TL;DR

This paper derives an inequality for the maximum work extractable from non-equilibrium steady states in one-dimensional quantum lattice systems, aligning with the second law of thermodynamics and extending understanding of quantum thermodynamic limits.

Contribution

It introduces a new inequality bounding work extraction in quantum lattice systems under non-equilibrium conditions, generalizing thermodynamic principles to quantum many-body systems.

Findings

Upper bound of work extraction tends to zero in equilibrium.

Bound depends on system model and reservoir temperatures.

Inequality reproduces classical second law in quantum context.

Abstract

We consider the Non-Equilibrium Steady State induced by two infinite quantum thermal reservoirs at different temperatures and derive an inequality giving the upper bound of the work extracted by cyclic operations. This upper bound tends to 0 in the equilibrium limit and the inequality reproduces the second law of thermodynamics that one cannot extract any work from equilibrium states by cyclic operations. In addition, we consider global cyclic operations and obtain an upper bound of the work density in one-dimensional quantum lattice systems, which depends on the model and the temperatures of the reservoirs. This bound is independent of the operations and also tends to 0 in the equilibrium limit.