{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T15:41:56Z","timestamp":1778859716057,"version":"3.51.4"},"reference-count":96,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,10,29]],"date-time":"2023-10-29T00:00:00Z","timestamp":1698537600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of education","award":["M\u0160MT RVO 14000"],"award-info":[{"award-number":["M\u0160MT RVO 14000"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>By employing Tsallis\u2019 extensive but non-additive \u03b4-entropy, we formulate the first two laws of thermodynamics for gravitating systems. By invoking Carath\u00e9odory\u2019s principle, we pay particular attention to the integrating factor for the heat one-form. We show that the latter factorizes into the product of thermal and entropic parts, where the entropic part cannot be reduced to a constant, as is the case in conventional thermodynamics, due to the non-additive nature of S\u03b4. The ensuing two laws of thermodynamics imply a Tsallis cosmology, which is then applied to a radiation-dominated universe to address the Big Bang nucleosynthesis and the relic abundance of cold dark matter particles. It is demonstrated that the Tsallis cosmology with the scaling exponent \u03b4\u223c1.499 (or equivalently, the anomalous dimension \u0394\u223c0.0013) consistently describes both the abundance of cold dark matter particles and the formation of primordial light elements, such as deuterium 2H and helium 4He. Salient issues, including the zeroth law of thermodynamics for the \u03b4-entropy and the lithium 7Li problem, are also briefly discussed.<\/jats:p>","DOI":"10.3390\/e25111495","type":"journal-article","created":{"date-parts":[[2023,10,30]],"date-time":"2023-10-30T12:07:45Z","timestamp":1698667665000},"page":"1495","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["Constraints on Tsallis Cosmology from Big Bang Nucleosynthesis and the Relic Abundance of Cold Dark Matter Particles"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7940-204X","authenticated-orcid":false,"given":"Petr","family":"Jizba","sequence":"first","affiliation":[{"name":"Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, B\u0159ehov\u00e1 7, 115 19 Praha, Czech Republic"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7574-2330","authenticated-orcid":false,"given":"Gaetano","family":"Lambiase","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica \u201cE.R. Caianiello\u201d, Universita\u2019 di Salerno, I-84084 Fisciano, SA, Italy"},{"name":"INFN\u2014Gruppo Collegato di Salerno, I-84084 Fisciano, SA, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2333","DOI":"10.1103\/PhysRevD.7.2333","article-title":"Black Holes and Entropy","volume":"7","author":"Bekenstein","year":"1973","journal-title":"Phys. Rev. D"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/BF02345020","article-title":"Particle creation by black holes","volume":"43","author":"Hawking","year":"1975","journal-title":"Comm. Math. Phys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1260","DOI":"10.1103\/PhysRevLett.75.1260","article-title":"Thermodynamics of space-time: The Einstein equation of state","volume":"75","author":"Jacobson","year":"1995","journal-title":"Phys. Rev. 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