{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:12:34Z","timestamp":1760242354831,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2017,5,6]],"date-time":"2017-05-06T00:00:00Z","timestamp":1494028800000},"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>A dynamical estimate is given for the Boltzmann entropy of the Universe, under the simplifying assumptions provided by Newtonian cosmology. We first model the cosmological fluid as the probability fluid of a quantum-mechanical system. Next, following current ideas about the emergence of spacetime, we regard gravitational equipotentials as isoentropic surfaces. Therefore, gravitational entropy is proportional to the vacuum expectation value of the gravitational potential in a certain quantum state describing the matter contents of the Universe. The entropy of the matter sector can also be computed. While providing values of the entropy that turn out to be somewhat higher than existing estimates, our results are in perfect compliance with the upper bound set by the holographic principle.<\/jats:p>","DOI":"10.3390\/e19050212","type":"journal-article","created":{"date-parts":[[2017,5,8]],"date-time":"2017-05-08T11:45:16Z","timestamp":1494243916000},"page":"212","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Boltzmann Entropy of a Newtonian Universe"],"prefix":"10.3390","volume":"19","author":[{"given":"D.","family":"Cabrera","sequence":"first","affiliation":[{"name":"Instituto Universitario de Matem\u00e1tica Pura y Aplicada, Universidad Polit\u00e9cnica de Valencia, Valencia 46022, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0347-7280","authenticated-orcid":false,"given":"Pedro","family":"Fern\u00e1ndez de C\u00f3rdoba","sequence":"additional","affiliation":[{"name":"Instituto Universitario de Matem\u00e1tica Pura y Aplicada, Universidad Polit\u00e9cnica de Valencia, Valencia 46022, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0720-9945","authenticated-orcid":false,"given":"J.M.","family":"Isidro","sequence":"additional","affiliation":[{"name":"Instituto Universitario de Matem\u00e1tica Pura y Aplicada, Universidad Polit\u00e9cnica de Valencia, Valencia 46022, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,5,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Adler, S. 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