{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T15:20:20Z","timestamp":1778944820696,"version":"3.51.4"},"reference-count":44,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2018,7,25]],"date-time":"2018-07-25T00:00:00Z","timestamp":1532476800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The Gibbs Paradox is essentially a set of open questions as to how sameness of gases or fluids (or masses, more generally) are to be treated in thermodynamics and statistical mechanics. They have a variety of answers, some restricted to quantum theory (there is no classical solution), some to classical theory (the quantum case is different). The solution offered here applies to both in equal measure, and is based on the concept of particle indistinguishability (in the classical case, Gibbs\u2019 notion of \u2018generic phase\u2019). Correctly understood, it is the elimination of sequence position as a labelling device, where sequences enter at the level of the tensor (or Cartesian) product of one-particle state spaces. In both cases it amounts to passing to the quotient space under permutations. \u2018Distinguishability\u2019, in the sense in which it is usually used in classical statistical mechanics, is a mathematically convenient, but physically muddled, fiction.<\/jats:p>","DOI":"10.3390\/e20080552","type":"journal-article","created":{"date-parts":[[2018,7,25]],"date-time":"2018-07-25T08:28:47Z","timestamp":1532507327000},"page":"552","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["The Gibbs Paradox"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8292-3014","authenticated-orcid":false,"given":"Simon","family":"Saunders","sequence":"first","affiliation":[{"name":"Faculty of Philosophy, University of Oxford, Oxford OX2 6GG, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,7,25]]},"reference":[{"key":"ref_1","unstructured":"Gibbs, J. 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