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 et al 2008 Europhys. Lett. 83 30008), 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.
Highlights
The emergence of thermodynamic behaviour within quantum mechanical systems has attracted much attention in recent years [1, 2]
This framework is of considerable conceptual interest as it aims to extend the connection between entropy and heat to finite, out of equilibrium quantum systems
We have demonstrated that the energy flux formalism satisfies the second law of thermodynamics
Summary
The emergence of thermodynamic behaviour within quantum mechanical systems has attracted much attention in recent years [1, 2]. The conventional definition of work and heat for a quantum system evolving under a time-dependent Hamiltonian considers the change in the internal energy U of a system with associated density matrix ρ as U = Tr{ρH } + Tr{ρH} and identifies the first (second) term as the work (heat) flux [16]. We are interested in autonomous bipartite quantum systems in which the inherent quantum mechanical interaction between the two partitions results in internal transfer of energy This internal transfer can subsequently be identified as either a heat, or a work, flux [17,18,19]. By defining an effective local energy basis, heat (work) flux is identified with energy changes that (do not) alter the the local von Neumann entropy This framework is of considerable conceptual interest as it aims to extend the connection between entropy and heat to finite, out of equilibrium quantum systems. The present work strengthens the energy flux formalism and provides further evidence that thermodynamic quantities such as work and heat can be generalized to quantum systems far from thermal equilibrium
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