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Entropy 2017, 19(6), 241; doi:10.3390/e19060241

Axiomatic Characterization of the Quantum Relative Entropy and Free Energy

Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
Authors to whom correspondence should be addressed.
Academic Editor: Ronnie Kosloff
Received: 6 April 2017 / Revised: 3 May 2017 / Accepted: 16 May 2017 / Published: 23 May 2017
(This article belongs to the Special Issue Quantum Thermodynamics)
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Building upon work by Matsumoto, we show that the quantum relative entropy with full-rank second argument is determined by four simple axioms: (i) Continuity in the first argument; (ii) the validity of the data-processing inequality; (iii) additivity under tensor products; and (iv) super-additivity. This observation has immediate implications for quantum thermodynamics, which we discuss. Specifically, we demonstrate that, under reasonable restrictions, the free energy is singled out as a measure of athermality. In particular, we consider an extended class of Gibbs-preserving maps as free operations in a resource-theoretic framework, in which a catalyst is allowed to build up correlations with the system at hand. The free energy is the only extensive and continuous function that is monotonic under such free operations. View Full-Text
Keywords: quantum relative entropy; non-equilibrium free energy; quantum thermodynamics; correlations quantum relative entropy; non-equilibrium free energy; quantum thermodynamics; correlations
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Wilming, H.; Gallego, R.; Eisert, J. Axiomatic Characterization of the Quantum Relative Entropy and Free Energy. Entropy 2017, 19, 241.

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