{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T00:48:00Z","timestamp":1778892480076,"version":"3.51.4"},"reference-count":73,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,1,28]],"date-time":"2021-01-28T00:00:00Z","timestamp":1611792000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In recent years, the implications of the generalized (GUP) and extended (EUP) uncertainty principles on Maxwell\u2013Boltzmann distribution have been widely investigated. However, at high energy regimes, the validity of Maxwell\u2013Boltzmann statistics is under debate and instead, the J\u00fcttner distribution is proposed as the distribution function in relativistic limit. Motivated by these considerations, in the present work, our aim is to study the effects of GUP and EUP on a system that obeys the J\u00fcttner distribution. To achieve this goal, we address a method to get the distribution function by starting from the partition function and its relation with thermal energy which finally helps us in finding the corresponding energy density states.<\/jats:p>","DOI":"10.3390\/sym13020213","type":"journal-article","created":{"date-parts":[[2021,1,28]],"date-time":"2021-01-28T09:03:45Z","timestamp":1611824625000},"page":"213","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["A Note on Effects of Generalized and Extended Uncertainty Principles on J\u00fcttner Gas"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0941-8422","authenticated-orcid":false,"given":"Hooman","family":"Moradpour","sequence":"first","affiliation":[{"name":"Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), University of Maragheh, Maragheh P.O. Box 55136-553, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sarah","family":"Aghababaei","sequence":"additional","affiliation":[{"name":"Department of Physics, Faculty of Sciences, Yasouj University, Yasouj 75918-74934, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7029-134X","authenticated-orcid":false,"given":"Amir Hadi","family":"Ziaie","sequence":"additional","affiliation":[{"name":"Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), University of Maragheh, Maragheh P.O. Box 55136-553, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5182","DOI":"10.1103\/PhysRevD.49.5182","article-title":"Quantum groups, gravity, and the generalized uncertainty principle","volume":"49","author":"Maggiore","year":"1994","journal-title":"Phys. Rev. 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