{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T01:17:28Z","timestamp":1779153448865,"version":"3.51.4"},"reference-count":41,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,1,25]],"date-time":"2024-01-25T00:00:00Z","timestamp":1706140800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001870","name":"Foundation for Polish Science","doi-asserted-by":"publisher","award":["2018\/MAB\/5"],"award-info":[{"award-number":["2018\/MAB\/5"]}],"id":[{"id":"10.13039\/501100001870","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001870","name":"Foundation for Polish Science","doi-asserted-by":"publisher","award":["465469\/2014-0"],"award-info":[{"award-number":["465469\/2014-0"]}],"id":[{"id":"10.13039\/501100001870","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001870","name":"Foundation for Polish Science","doi-asserted-by":"publisher","award":["308065\/2022-0"],"award-info":[{"award-number":["308065\/2022-0"]}],"id":[{"id":"10.13039\/501100001870","id-type":"DOI","asserted-by":"publisher"}]},{"name":"EU","award":["2018\/MAB\/5"],"award-info":[{"award-number":["2018\/MAB\/5"]}]},{"name":"EU","award":["465469\/2014-0"],"award-info":[{"award-number":["465469\/2014-0"]}]},{"name":"EU","award":["308065\/2022-0"],"award-info":[{"award-number":["308065\/2022-0"]}]},{"name":"National Institute for the Science and Technology of Quantum Information (INCT-IQ)","award":["2018\/MAB\/5"],"award-info":[{"award-number":["2018\/MAB\/5"]}]},{"name":"National Institute for the Science and Technology of Quantum Information (INCT-IQ)","award":["465469\/2014-0"],"award-info":[{"award-number":["465469\/2014-0"]}]},{"name":"National Institute for the Science and Technology of Quantum Information (INCT-IQ)","award":["308065\/2022-0"],"award-info":[{"award-number":["308065\/2022-0"]}]},{"DOI":"10.13039\/501100003593","name":"National Council for Scientific and Technological Development (CNPq)","doi-asserted-by":"publisher","award":["2018\/MAB\/5"],"award-info":[{"award-number":["2018\/MAB\/5"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003593","name":"National Council for Scientific and Technological Development (CNPq)","doi-asserted-by":"publisher","award":["465469\/2014-0"],"award-info":[{"award-number":["465469\/2014-0"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003593","name":"National Council for Scientific and Technological Development (CNPq)","doi-asserted-by":"publisher","award":["308065\/2022-0"],"award-info":[{"award-number":["308065\/2022-0"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Coordination of Superior Level Staff Improvement (CAPES)","award":["2018\/MAB\/5"],"award-info":[{"award-number":["2018\/MAB\/5"]}]},{"name":"Coordination of Superior Level Staff Improvement (CAPES)","award":["465469\/2014-0"],"award-info":[{"award-number":["465469\/2014-0"]}]},{"name":"Coordination of Superior Level Staff Improvement (CAPES)","award":["308065\/2022-0"],"award-info":[{"award-number":["308065\/2022-0"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The universality of classical thermodynamics rests on the central limit theorem, due to which, measurements of thermal fluctuations are unable to reveal detailed information regarding the microscopic structure of a macroscopic body. When small systems are considered and fluctuations become important, thermodynamic quantities can be understood in the context of classical stochastic mechanics. A fundamental assumption behind thermodynamics is therefore that of coarse graining, which stems from a substantial lack of control over all degrees of freedom. However, when quantum systems are concerned, one claims a high level of control. As a consequence, information theory plays a major role in the identification of thermodynamic functions. Here, drawing from the concept of gauge symmetry\u2014essential in all modern physical theories\u2014we put forward a new possible intermediate route. Working within the realm of quantum thermodynamics, we explicitly construct physically motivated gauge transformations which encode a gentle variant of coarse graining behind thermodynamics. As a first application of this new framework, we reinterpret quantum work and heat, as well as the role of quantum coherence.<\/jats:p>","DOI":"10.3390\/e26020111","type":"journal-article","created":{"date-parts":[[2024,1,25]],"date-time":"2024-01-25T10:32:38Z","timestamp":1706178758000},"page":"111","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Gauge-Invariant Quantum Thermodynamics: Consequences for the First Law"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5120-8176","authenticated-orcid":false,"given":"Lucas C.","family":"C\u00e9leri","sequence":"first","affiliation":[{"name":"QPequi Group, Institute of Physics, Federal University of Goi\u00e1s, Goi\u00e2nia 74690-900, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"\u0141ukasz","family":"Rudnicki","sequence":"additional","affiliation":[{"name":"International Centre for Theory of Quantum Technologies (ICTQT), University of Gda\u0144sk, 80-308 Gda\u0144sk, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,25]]},"reference":[{"key":"ref_1","unstructured":"Callen, H.B. 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