{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,22]],"date-time":"2026-03-22T12:09:49Z","timestamp":1774181389141,"version":"3.50.1"},"reference-count":38,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,12,18]],"date-time":"2024-12-18T00:00:00Z","timestamp":1734480000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Austrian Science Fund (FWF)","award":["10.55776\/CO3"],"award-info":[{"award-number":["10.55776\/CO3"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>It is customary to classify approaches in statistical mechanics (SM) as belonging either to Boltzmanninan SM (BSM) or Gibbsian SM (GSM). It is, however, unclear how the Boltzmann equation (BE) fits into either of these approaches. To discuss the relation between BE and BSM, we first present a version of BSM that differs from standard presentation in that it uses local field variables to individuate macro-states, and we then show that BE is a special case of BSM thus understood. To discuss the relation between BE and GSM, we focus on the BBGKY hierarchy and note the version of the BE that follows from the hierarchy is \u201cGibbsian\u201d only in the minimal sense that it operates with an invariant measure on the state space of the full system.<\/jats:p>","DOI":"10.3390\/e26121106","type":"journal-article","created":{"date-parts":[[2024,12,18]],"date-time":"2024-12-18T08:56:32Z","timestamp":1734512192000},"page":"1106","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["The Boltzmann Equation and Its Place in the Edifice of Statistical Mechanics"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2980-8436","authenticated-orcid":false,"given":"Charlotte","family":"Werndl","sequence":"first","affiliation":[{"name":"Department of Philosophy, Faculty of Social Sciences, University of Salzburg, Franziskanergasse 1, 5020 Salzburg, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0812-0907","authenticated-orcid":false,"given":"Roman","family":"Frigg","sequence":"additional","affiliation":[{"name":"Department of Philosophy, Logic and Scientific Method, London School of Economics, Houghton Street, London WC2A 2AE, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,18]]},"reference":[{"key":"ref_1","first-page":"275","article-title":"Weitere Studien \u00fcber das W\u00e4rmegleichgewicht unter Gasmolek\u00fcle","volume":"66","author":"Boltzmann","year":"1872","journal-title":"Wien. 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