{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T18:10:50Z","timestamp":1770487850628,"version":"3.49.0"},"reference-count":30,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2017,5,23]],"date-time":"2017-05-23T00:00:00Z","timestamp":1495497600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100017325","name":"ERC","doi-asserted-by":"publisher","award":["TAQ"],"award-info":[{"award-number":["TAQ"]}],"id":[{"id":"10.13039\/100017325","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100004875","name":"DFG","doi-asserted-by":"publisher","award":["GA 2184\/2-1"],"award-info":[{"award-number":["GA 2184\/2-1"]}],"id":[{"id":"10.13039\/100004875","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100016077","name":"EU","doi-asserted-by":"publisher","award":["COST MP1209"],"award-info":[{"award-number":["COST MP1209"]}],"id":[{"id":"10.13039\/100016077","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100016077","name":"EU","doi-asserted-by":"publisher","award":["AQuS"],"award-info":[{"award-number":["AQuS"]}],"id":[{"id":"10.13039\/100016077","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004350","name":"Studienstiftung des Deutschen Volkes","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004350","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/e19060241","type":"journal-article","created":{"date-parts":[[2017,5,23]],"date-time":"2017-05-23T11:14:33Z","timestamp":1495538073000},"page":"241","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":40,"title":["Axiomatic Characterization of the Quantum Relative Entropy and Free Energy"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0306-7679","authenticated-orcid":false,"given":"Henrik","family":"Wilming","sequence":"first","affiliation":[{"name":"Dahlem Center for Complex Quantum Systems, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany"}]},{"given":"Rodrigo","family":"Gallego","sequence":"additional","affiliation":[{"name":"Dahlem Center for Complex Quantum Systems, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany"}]},{"given":"Jens","family":"Eisert","sequence":"additional","affiliation":[{"name":"Dahlem Center for Complex Quantum Systems, Freie Universit\u00e4t Berlin, 14195 Berlin, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2017,5,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hiai, F., and Petz, D. 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