Work, heat and entropy production in bipartite quantum systems

TL;DR

This paper explores how commutation relations in bipartite quantum systems influence work, heat, and entropy production, extending the formalism to open systems and reconciling with the second law of thermodynamics.

Contribution

It introduces a detailed analysis of work, heat, and entropy in bipartite quantum systems considering specific commutation relations, and extends the framework to open systems with thermal baths.

Findings

Commutation relations constrain energy fluxes between subsystems.

The formalism is extended to include Markovian thermal baths.

The approach is reconciled with the second law of thermodynamics.

Abstract

In bipartite quantum systems commutation relations between the Hamiltonian of each subsystem and the interaction impose fundamental constraints on the dynamics of each partition. Here we investigate work, heat and entropy production in bipartite systems characterized by particular commutators between their local Hamiltonians and the interaction operator. We consider the formalism of [Weimer, EPL, 83:30008, 2008], in which heat (work) is identified with energy changes that (do not) alter the local von Neumann entropy, as observed in an effective local measurement basis. We demonstrate the consequences of the commutation relations on the work and heat fluxes into each partition, and extend the formalism to open quantum systems where one, or both, partitions are subject to a Markovian thermal bath. We also discuss the relation between heat and entropy in bipartite quantum systems out of thermal equilibrium, and reconcile the aforementioned approach with the second law of thermodynamics.