{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:19:54Z","timestamp":1760242794537,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2016,7,13]],"date-time":"2016-07-13T00:00:00Z","timestamp":1468368000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100010198","name":"MINECO","doi-asserted-by":"publisher","award":["FIS2015-63268-C2-2-R"],"award-info":[{"award-number":["FIS2015-63268-C2-2-R"]}],"id":[{"id":"10.13039\/501100010198","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Statistics of distinguishable particles has become relevant in systems of colloidal particles and in the context of applications of statistical mechanics to complex networks. In this paper, we present evidence that a commonly used expression for the partition function of a system of distinguishable particles leads to huge fluctuations of the number of particles in the grand canonical ensemble and, consequently, to nonequivalence of statistical ensembles. We will show that the alternative definition of the partition function including, naturally, Boltzmann\u2019s correct counting factor for distinguishable particles solves the problem and restores ensemble equivalence. Finally, we also show that this choice for the partition function does not produce any inconsistency for a system of distinguishable localized particles, where the monoparticular partition function is not extensive.<\/jats:p>","DOI":"10.3390\/e18070259","type":"journal-article","created":{"date-parts":[[2016,7,13]],"date-time":"2016-07-13T09:48:45Z","timestamp":1468403325000},"page":"259","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Ensemble Equivalence for Distinguishable Particles"],"prefix":"10.3390","volume":"18","author":[{"given":"Antonio","family":"Fern\u00e1ndez-Peralta","sequence":"first","affiliation":[{"name":"Instituto de F\u00edsica Interdisciplinar y Sistemas Complejos (IFISC), Consejo Superior de Investigaciones Cient\u00edficas (CSIC)\u2013Universitat de les Illes Balears (UIB), Palma de Mallorca 07122, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ra\u00fal","family":"Toral","sequence":"additional","affiliation":[{"name":"Instituto de F\u00edsica Interdisciplinar y Sistemas Complejos (IFISC), Consejo Superior de Investigaciones Cient\u00edficas (CSIC)\u2013Universitat de les Illes Balears (UIB), Palma de Mallorca 07122, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,7,13]]},"reference":[{"unstructured":"Pathria, R.K., and Beale, P.D. 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Equilibrium and Non-Equilibrium Statistical Mechanics, John Wiley & Sons.","key":"ref_23"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/18\/7\/259\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:26:00Z","timestamp":1760210760000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/18\/7\/259"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,7,13]]},"references-count":23,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2016,7]]}},"alternative-id":["e18070259"],"URL":"https:\/\/doi.org\/10.3390\/e18070259","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2016,7,13]]}}}