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arXiv:1601.01302 · Physical Review X

Fully Quantum Fluctuation Theorems

Johan Åberg

Published Feb 6, 2018• 122 citations
arXivHTMLPDF

Abstract

A new generalization of Crooks fluctuation theorem, which describes randomness in thermodynamic work, incorporates both thermal and quantum phenomena---a key step in understanding the dynamics of single molecules and atoms.
DOI
10.1103/physrevx.8.011019

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Fluctuation theorems provide universal constraints on nonequilibrium energy and entropy fluctuations, making them a natural framework to assess how and to what extent quantum resources become thermodynamically relevant. We develop a unified framework for incorporating a generic quantum resource, including athermality, quantum coherence, and entanglement, into fluctuation theorems. We work within the end point measurement scheme, which avoids an initial energy measurement and allows quantum resources in the initial state to affect nonequilibrium energy statistics. We derive a family of quantum fluctuation theorems, including generalized Jarzynski equalities and Crooks type fluctuation relations, in which corrections decompose into resource resolved contributions. For single systems, we introduce the concept of weight of athermality, and combine it with the weight of coherence to isolate distinct thermodynamic effects of these quantum resources. For bipartite systems, we furthermore obtain two families of entanglement-resolved fluctuation theorems using an appended correlation operator and the best separable approximation, respectively. Finally, we introduce the concepts of coherence and entanglement fluctuation distances, as Kullback Leibler divergences, which quantify the thermodynamic relevance of quantum resources in a process-dependent and operational manner.
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Fluctuation theorems for work provide universal constraints on nonequilibrium fluctuations, yet their quantum generalizations often rely on externally prescribed classical driving protocols. While for classical systems, fluctuation theorems have been extended to autonomous work, where the dynamics of the work source is subject to the backaction of the system, their generalization to the quantum regime is constrained by the uncertainty principle. Here, we extend fluctuation theorems for autonomous work from the classical regime to the quantum regime. By performing successive projective measurements over the work source and the system, we derive Jarzynski-type and Crooks-type fluctuation theorems for autonomous inclusive work from initial mixed thermal states. These relations are analogous to fluctuation theorems for autonomous work in the classical regime and explicitly incorporate the fluctuations of the work source. However, quantum noncommutativity prevents a consistent reduction to the nonautonomous counterparts, even in the limit of a large work source and correspondingly negligible backaction. By contrast, under the exclusive work definition, the nonautonomous limit is recovered when the measured observable of the work source commutes with its bare Hamiltonian and the backaction of the system on the work source is negligible. Our results are illustrated with the Dicke model, where a single-mode radiation field and an ensemble of two-level atoms act as the system of interest and the work source, respectively.