{"id":"https://openalex.org/W4393044498","doi":"https://doi.org/10.3390/e26030273","title":"Tsallis Distribution as a \u039b-Deformation of the Maxwell\u2013J\u00fcttner Distribution","display_name":"Tsallis Distribution as a \u039b-Deformation of the Maxwell\u2013J\u00fcttner Distribution","publication_year":2024,"publication_date":"2024-03-21","ids":{"openalex":"https://openalex.org/W4393044498","doi":"https://doi.org/10.3390/e26030273","pmid":"https://pubmed.ncbi.nlm.nih.gov/38539784"},"language":"en","primary_location":{"id":"doi:10.3390/e26030273","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e26030273","pdf_url":"https://www.mdpi.com/1099-4300/26/3/273/pdf?version=1711013245","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/26/3/273/pdf?version=1711013245","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063248731","display_name":"Jean\u2010Pierre Gazeau","orcid":"https://orcid.org/0000-0001-7681-7672"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I2802090066","display_name":"Laboratoire AstroParticule et Cosmologie","ror":"https://ror.org/03tnjrr49","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I2738703131","https://openalex.org/I2746051580","https://openalex.org/I2799535048","https://openalex.org/I2800004676","https://openalex.org/I2802090066","https://openalex.org/I4210133362"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Jean-Pierre Gazeau","raw_affiliation_strings":["Centre National de la Recherche Scientifique (CNRS), Astroparticule et Cosmologie, Universit\u00e9 Paris Cit\u00e9, F-75013 Paris, France"],"raw_orcid":"https://orcid.org/0000-0001-7681-7672","affiliations":[{"raw_affiliation_string":"Centre National de la Recherche Scientifique (CNRS), Astroparticule et Cosmologie, Universit\u00e9 Paris Cit\u00e9, F-75013 Paris, France","institution_ids":["https://openalex.org/I2802090066","https://openalex.org/I204730241","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5063248731"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I2802090066"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.2495,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.47759439,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"26","issue":"3","first_page":"273","last_page":"273"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10095","display_name":"Cosmology and Gravitation Theories","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10527","display_name":"High-Energy Particle Collisions Research","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.7930374145507812},{"id":"https://openalex.org/keywords/cosmological-constant","display_name":"Cosmological constant","score":0.6761507987976074},{"id":"https://openalex.org/keywords/tsallis-statistics","display_name":"Tsallis statistics","score":0.6748189926147461},{"id":"https://openalex.org/keywords/cosmology","display_name":"Cosmology","score":0.5492956638336182},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.49169307947158813},{"id":"https://openalex.org/keywords/theoretical-physics","display_name":"Theoretical physics","score":0.4884154200553894},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.48643994331359863},{"id":"https://openalex.org/keywords/de-sitter-universe","display_name":"De Sitter universe","score":0.4701889753341675},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.41354191303253174},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.4084044098854065},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3962283134460449},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3935154378414154},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.3032264709472656},{"id":"https://openalex.org/keywords/universe","display_name":"Universe","score":0.22084927558898926},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09237700700759888},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.08865317702293396}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.7930374145507812},{"id":"https://openalex.org/C166861157","wikidata":"https://www.wikidata.org/wiki/Q59151","display_name":"Cosmological constant","level":2,"score":0.6761507987976074},{"id":"https://openalex.org/C2780056601","wikidata":"https://www.wikidata.org/wiki/Q7849339","display_name":"Tsallis statistics","level":2,"score":0.6748189926147461},{"id":"https://openalex.org/C26405456","wikidata":"https://www.wikidata.org/wiki/Q338","display_name":"Cosmology","level":2,"score":0.5492956638336182},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.49169307947158813},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.4884154200553894},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.48643994331359863},{"id":"https://openalex.org/C19262093","wikidata":"https://www.wikidata.org/wiki/Q3036474","display_name":"De Sitter universe","level":3,"score":0.4701889753341675},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.41354191303253174},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.4084044098854065},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3962283134460449},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3935154378414154},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3032264709472656},{"id":"https://openalex.org/C84999194","wikidata":"https://www.wikidata.org/wiki/Q1","display_name":"Universe","level":2,"score":0.22084927558898926},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09237700700759888},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.08865317702293396},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3390/e26030273","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e26030273","pdf_url":"https://www.mdpi.com/1099-4300/26/3/273/pdf?version=1711013245","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:38539784","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/38539784","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:10969626","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/10969626","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC10969626/pdf/entropy-26-00273.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:HAL:hal-04536238v1","is_oa":false,"landing_page_url":"https://hal.science/hal-04536238","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, 2024, 26 (3), pp.273. &#x27E8;10.3390/e26030273&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:doaj.org/article:3a452ebaaa574c18b3bc2de3ea84fff5","is_oa":true,"landing_page_url":"https://doaj.org/article/3a452ebaaa574c18b3bc2de3ea84fff5","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 26, Iss 3, p 273 (2024)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/26/3/273/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e26030273","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e26030273","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e26030273","pdf_url":"https://www.mdpi.com/1099-4300/26/3/273/pdf?version=1711013245","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4393044498.pdf"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1529934007","https://openalex.org/W1556192255","https://openalex.org/W1968930637","https://openalex.org/W1980097479","https://openalex.org/W1983874169","https://openalex.org/W1985916365","https://openalex.org/W2003044663","https://openalex.org/W2008184201","https://openalex.org/W2011180185","https://openalex.org/W2035115555","https://openalex.org/W2046286337","https://openalex.org/W2048886530","https://openalex.org/W2085166342","https://openalex.org/W2088336775","https://openalex.org/W2095228741","https://openalex.org/W2151524917","https://openalex.org/W2257289106","https://openalex.org/W2952960441","https://openalex.org/W3106359821","https://openalex.org/W3123013846","https://openalex.org/W3123204788","https://openalex.org/W4245986608","https://openalex.org/W4306253255","https://openalex.org/W4310625165","https://openalex.org/W7000791799"],"related_works":["https://openalex.org/W2954782866","https://openalex.org/W1807971224","https://openalex.org/W3103332506","https://openalex.org/W2894459085","https://openalex.org/W4316813051","https://openalex.org/W2562902620","https://openalex.org/W4312107329","https://openalex.org/W2102647021","https://openalex.org/W3100001996","https://openalex.org/W3098371892"],"abstract_inverted_index":{"Currently,":[0],"there":[1],"is":[2,28,37,67,121,130],"no":[3],"widely":[4],"accepted":[5],"consensus":[6],"regarding":[7],"a":[8,48,85,110,131,145],"consistent":[9],"thermodynamic":[10],"framework":[11,98],"within":[12,77,96],"the":[13,21,40,53,60,63,74,78,97,105,113,122,126,135,149,155,161],"special":[14],"relativity":[15],"paradigm.":[16],"However,":[17],"by":[18,69,117],"postulating":[19],"that":[20,39],"inverse":[22],"temperature":[23],"4-vector,":[24],"denoted":[25],"as":[26,47],"\u03b2,":[27],"future-directed":[29],"and":[30,95,128,154,167],"time-like,":[31],"intriguing":[32],"insights":[33],"emerge.":[34],"Specifically,":[35],"it":[36],"demonstrated":[38],"q-dependent":[41],"Tsallis":[42,106,150],"distribution":[43],"can":[44],"be":[45],"conceptualized":[46],"de":[49,64,102],"Sitterian":[50,103],"deformation":[51],"of":[52,62,89,99,125,137],"relativistic":[54,165],"Maxwell\u2013J\u00fcttner":[55],"distribution.":[56],"In":[57],"this":[58],"context,":[59],"curvature":[61],"Sitter":[65],"space-time":[66],"characterized":[68],"\u039b/3,":[70],"where":[71,119],"\u039b":[72],"represents":[73],"cosmological":[75,114,156,169],"constant":[76,115],"\u039bCDM":[79],"standard":[80],"model":[81],"for":[82],"cosmology.":[83],"For":[84],"simple":[86],"gas":[87],"composed":[88],"particles":[90],"with":[91],"proper":[92],"mass":[93],"m,":[94],"quantum":[100,152],"statistical":[101],"considerations,":[104],"parameter":[107],"q":[108],"exhibits":[109],"dependence":[111],"on":[112,160],"given":[116],"q=1+\u2113c\u039b/n,":[118],"\u2113c=\u210f/mc":[120],"Compton":[123],"length":[124],"particle":[127],"n":[129],"positive":[132],"numerical":[133],"factor,":[134],"determination":[136],"which":[138],"awaits":[139],"observational":[140],"confirmation.":[141],"This":[142],"formulation":[143],"establishes":[144],"novel":[146],"connection":[147],"between":[148,164],"distribution,":[151],"statistics,":[153],"constant,":[157],"shedding":[158],"light":[159],"intricate":[162],"interplay":[163],"thermodynamics":[166],"fundamental":[168],"parameters.":[170]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-06-13T06:13:01.061226","created_date":"2025-10-10T00:00:00"}
