Axiomatic characterization of the quantum relative entropy and free energy
Wilming H, Gallego R, Eisert J (2017)
Publication Type: Journal article
Publication year: 2017
Journal
Book Volume: 19
Article Number: 241
Journal Issue: 6
DOI: 10.3390/e19060241
Abstract
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.
Involved external institutions
Germany (DE)How to cite
APA:
Wilming, H., Gallego, R., & Eisert, J. (2017). Axiomatic characterization of the quantum relative entropy and free energy. Entropy, 19(6). https://doi.org/10.3390/e19060241
MLA:
Wilming, Henrik, Rodrigo Gallego, and Jens Eisert. "Axiomatic characterization of the quantum relative entropy and free energy." Entropy 19.6 (2017).
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