Periodic thermodynamics of open quantum systems

Kay Brandner, Udo Seifert

Research output: Contribution to journalArticleScientificpeer-review

47 Citations (Scopus)
163 Downloads (Pure)


The thermodynamics of quantum systems coupled to periodically modulated heat baths and work reservoirs is developed. By identifying affinities and fluxes, the first and the 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 an additional 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 cannot 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.

Original languageEnglish
Article number062134
Pages (from-to)1-20
JournalPhysical Review E
Issue number6
Publication statusPublished - 22 Jun 2016
MoE publication typeA1 Journal article-refereed

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