Periodic Thermodynamics of Open Quantum Systems

TL;DR

This paper develops a thermodynamic framework for open quantum systems under periodic driving, establishing laws, reciprocity, and bounds on efficiency, especially highlighting the impact of quantum coherence on heat engine performance.

Contribution

It introduces a comprehensive thermodynamic theory for periodically driven quantum systems, including new bounds on efficiency influenced by quantum coherence effects.

Findings

Entropy production is quadratic in affinities in linear response.

Reciprocity relations are derived from time-reversal symmetry.

Quantum coherence limits the maximum efficiency below Carnot's bound.

Abstract

The thermodynamics of quantum systems coupled to periodically modulated heat baths and work reservoirs is developed. By identifying affinities and fluxes, the first and second law are formulated consistently. In the linear response regime, entropy production becomes a quadratic form in the affinities. Specializing to Lindblad-dynamics, we identify the corresponding kinetic coefficients in terms of correlation functions of the unperturbed dynamics. Reciprocity relations follow from symmetries with respect to time reversal. The kinetic coefficients can be split into a classical and a quantum contribution subject to a new constraint, which follows from a natural detailed balance condition. This constraint implies universal bounds on efficiency and power of quantum heat engines. In particular, we show that Carnot efficiency can not be reached whenever quantum coherence effects are present, i.e., when the Hamiltonian used for work extraction does not commute with the bare system Hamiltonian. For illustration, we specialize our universal results to a driven two-level system in contact with a heat bath of sinusoidally modulated temperature.