{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T06:55:53Z","timestamp":1781247353188,"version":"3.54.1"},"reference-count":28,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,3,21]],"date-time":"2024-03-21T00:00:00Z","timestamp":1710979200000},"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>Currently, there is no widely accepted consensus regarding a consistent thermodynamic framework within the special relativity paradigm. However, by postulating that the inverse temperature 4-vector, denoted as \u03b2, is future-directed and time-like, intriguing insights emerge. Specifically, it is demonstrated that the q-dependent Tsallis distribution can be conceptualized as a de Sitterian deformation of the relativistic Maxwell\u2013J\u00fcttner distribution. In this context, the curvature of the de Sitter space-time is characterized by \u039b\/3, where \u039b represents the cosmological constant within the \u039bCDM standard model for cosmology. For a simple gas composed of particles with proper mass m, and within the framework of quantum statistical de Sitterian considerations, the Tsallis parameter q exhibits a dependence on the cosmological constant given by q=1+\u2113c\u039b\/n, where \u2113c=\u210f\/mc is the Compton length of the particle and n is a positive numerical factor, the determination of which awaits observational confirmation. This formulation establishes a novel connection between the Tsallis distribution, quantum statistics, and the cosmological constant, shedding light on the intricate interplay between relativistic thermodynamics and fundamental cosmological parameters.<\/jats:p>","DOI":"10.3390\/e26030273","type":"journal-article","created":{"date-parts":[[2024,3,21]],"date-time":"2024-03-21T06:35:30Z","timestamp":1711002930000},"page":"273","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Tsallis Distribution as a \u039b-Deformation of the Maxwell\u2013J\u00fcttner Distribution"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7681-7672","authenticated-orcid":false,"given":"Jean-Pierre","family":"Gazeau","sequence":"first","affiliation":[{"name":"Centre National de la Recherche Scientifique (CNRS), Astroparticule et Cosmologie, Universit\u00e9 Paris Cit\u00e9, F-75013 Paris, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,21]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"Sur la variance relativiste de la temp\u00e9rature","volume":"31","year":"1948","journal-title":"Cah. 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