{"id":"https://openalex.org/W4200207299","doi":"https://doi.org/10.3390/e23121683","title":"Thermodynamic Definitions of Temperature and Kappa and Introduction of the Entropy Defect","display_name":"Thermodynamic Definitions of Temperature and Kappa and Introduction of the Entropy Defect","publication_year":2021,"publication_date":"2021-12-15","ids":{"openalex":"https://openalex.org/W4200207299","doi":"https://doi.org/10.3390/e23121683","pmid":"https://pubmed.ncbi.nlm.nih.gov/34945989"},"language":"en","primary_location":{"id":"doi:10.3390/e23121683","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23121683","pdf_url":"https://www.mdpi.com/1099-4300/23/12/1683/pdf?version=1639542065","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/1099-4300/23/12/1683/pdf?version=1639542065","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080379161","display_name":"G. Livadiotis","orcid":"https://orcid.org/0000-0002-7655-6019"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"George Livadiotis","raw_affiliation_strings":["Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA"],"raw_orcid":"https://orcid.org/0000-0002-7655-6019","affiliations":[{"raw_affiliation_string":"Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087930598","display_name":"D. J. McComas","orcid":"https://orcid.org/0000-0001-6160-1158"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David J. McComas","raw_affiliation_strings":["Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5080379161"],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":{"value":1800,"currency":"CHF","value_usd":1944},"apc_paid":{"value":1800,"currency":"CHF","value_usd":1944},"fwci":2.4775,"has_fulltext":true,"cited_by_count":35,"citation_normalized_percentile":{"value":0.9007124,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"23","issue":"12","first_page":"1683","last_page":"1683"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9998000264167786,"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":0.9998000264167786,"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/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9922000169754028,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9455000162124634,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.6355366110801697},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.6070388555526733},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5842635035514832},{"id":"https://openalex.org/keywords/kappa","display_name":"Kappa","score":0.5219470858573914},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.48718470335006714},{"id":"https://openalex.org/keywords/statistical-mechanics","display_name":"Statistical mechanics","score":0.44019615650177},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4374411702156067},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4347052574157715},{"id":"https://openalex.org/keywords/kinetic-energy","display_name":"Kinetic energy","score":0.42815494537353516},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.20979708433151245},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.143172025680542}],"concepts":[{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.6355366110801697},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.6070388555526733},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5842635035514832},{"id":"https://openalex.org/C2778724333","wikidata":"https://www.wikidata.org/wiki/Q14401","display_name":"Kappa","level":2,"score":0.5219470858573914},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.48718470335006714},{"id":"https://openalex.org/C99874945","wikidata":"https://www.wikidata.org/wiki/Q188715","display_name":"Statistical mechanics","level":2,"score":0.44019615650177},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4374411702156067},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4347052574157715},{"id":"https://openalex.org/C135889238","wikidata":"https://www.wikidata.org/wiki/Q46276","display_name":"Kinetic energy","level":2,"score":0.42815494537353516},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.20979708433151245},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.143172025680542},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e23121683","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23121683","pdf_url":"https://www.mdpi.com/1099-4300/23/12/1683/pdf?version=1639542065","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:34945989","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34945989","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":"Journal Article"},{"id":"pmh:oai:pubmedcentral.nih.gov:8700829","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/8700829","pdf_url":null,"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:doaj.org/article:6ff7ef9777ee43f29458cd45b1083170","is_oa":true,"landing_page_url":"https://doaj.org/article/6ff7ef9777ee43f29458cd45b1083170","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 23, Iss 12, p 1683 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e23121683","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23121683","pdf_url":"https://www.mdpi.com/1099-4300/23/12/1683/pdf?version=1639542065","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":[{"display_name":"Affordable and clean energy","score":0.5600000023841858,"id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G2279504566","display_name":null,"funder_award_id":"80NSSC20K0719","funder_id":"https://openalex.org/F4320306101","funder_display_name":"National Aeronautics and Space Administration"}],"funders":[{"id":"https://openalex.org/F4320306101","display_name":"National Aeronautics and Space Administration","ror":"https://ror.org/027ka1x80"},{"id":"https://openalex.org/F4320322037","display_name":"Nuclear Safety and Security Commission","ror":"https://ror.org/05qk3ge34"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4200207299.pdf","grobid_xml":"https://content.openalex.org/works/W4200207299.grobid-xml"},"referenced_works_count":79,"referenced_works":["https://openalex.org/W1553236419","https://openalex.org/W1586540887","https://openalex.org/W1862918737","https://openalex.org/W1964997025","https://openalex.org/W1965159161","https://openalex.org/W1967243981","https://openalex.org/W1980891956","https://openalex.org/W1983874169","https://openalex.org/W1983930467","https://openalex.org/W1985679876","https://openalex.org/W1986983422","https://openalex.org/W1992538900","https://openalex.org/W1993089110","https://openalex.org/W1997281911","https://openalex.org/W1997414622","https://openalex.org/W2000264375","https://openalex.org/W2003097973","https://openalex.org/W2009185635","https://openalex.org/W2009586635","https://openalex.org/W2015224222","https://openalex.org/W2017109395","https://openalex.org/W2017806270","https://openalex.org/W2018454770","https://openalex.org/W2027402993","https://openalex.org/W2033652368","https://openalex.org/W2034315815","https://openalex.org/W2035317159","https://openalex.org/W2035637366","https://openalex.org/W2036692471","https://openalex.org/W2039905978","https://openalex.org/W2040459036","https://openalex.org/W2046230514","https://openalex.org/W2047187965","https://openalex.org/W2047546246","https://openalex.org/W2047798490","https://openalex.org/W2050941779","https://openalex.org/W2057453691","https://openalex.org/W2065502108","https://openalex.org/W2070847964","https://openalex.org/W2071941889","https://openalex.org/W2072406744","https://openalex.org/W2080414626","https://openalex.org/W2080601053","https://openalex.org/W2081523618","https://openalex.org/W2086606944","https://openalex.org/W2089607375","https://openalex.org/W2089852843","https://openalex.org/W2098694238","https://openalex.org/W2111894009","https://openalex.org/W2112572275","https://openalex.org/W2144621465","https://openalex.org/W2147142925","https://openalex.org/W2170614585","https://openalex.org/W2470851072","https://openalex.org/W2516865766","https://openalex.org/W2524498983","https://openalex.org/W2625882416","https://openalex.org/W2759633664","https://openalex.org/W2785731430","https://openalex.org/W2790395485","https://openalex.org/W2801832422","https://openalex.org/W2807640218","https://openalex.org/W2884571279","https://openalex.org/W2891790758","https://openalex.org/W2904226061","https://openalex.org/W2914496275","https://openalex.org/W2943493148","https://openalex.org/W2972807672","https://openalex.org/W2979890006","https://openalex.org/W2995650169","https://openalex.org/W3098234806","https://openalex.org/W3098326078","https://openalex.org/W3112282218","https://openalex.org/W3112826380","https://openalex.org/W3134267190","https://openalex.org/W4249046827","https://openalex.org/W4300987473","https://openalex.org/W6689451202","https://openalex.org/W6720085970"],"related_works":["https://openalex.org/W1513518876","https://openalex.org/W3147051519","https://openalex.org/W1974744264","https://openalex.org/W1539053031","https://openalex.org/W2087072744","https://openalex.org/W2401822278","https://openalex.org/W2059075682","https://openalex.org/W2291331221","https://openalex.org/W1973177902","https://openalex.org/W2126551324"],"abstract_inverted_index":{"This":[0,119],"paper":[1],"develops":[2],"explicit":[3],"and":[4,14,25,151,186,189,208,210],"consistent":[5],"definitions":[6,148,159],"of":[7,12,21,32,43,52,60,63,66,96,149,170,177,199],"the":[8,15,19,30,37,41,49,58,61,94,97,127,132,137,156,168,192,212,220],"independent":[9],"thermodynamic":[10,147,200],"properties":[11],"temperature":[13,152,221],"kappa":[16,33,150,162,207],"index":[17],"within":[18],"framework":[20],"nonextensive":[22,50],"statistical":[23],"mechanics":[24],"shows":[26],"their":[27,64],"connection":[28],"with":[29,54,81,141,155,179],"formalism":[31],"distributions.":[34,163],"By":[35],"defining":[36],"\"entropy":[38],"defect\"":[39],"in":[40,197],"composition":[42],"a":[44,102,171,175],"system,":[45,172],"we":[46,165],"show":[47,166],"how":[48],"entropy":[51,123,169],"systems":[53],"correlations":[55],"differs":[56],"from":[57,161],"sum":[59,95],"entropies":[62],"constituents":[65],"these":[67],"systems.":[68],"A":[69],"system":[70,89,103],"is":[71,92,104,181],"composed":[72,105,173],"extensively":[73],"when":[74,107],"its":[75,108],"elementary":[76,109],"subsystems":[77,110,178],"are":[78,111],"independent,":[79],"interacting":[80],"no":[82],"correlations;":[83],"this":[84],"leads":[85,120],"to":[86,121,131,215,219],"an":[87,122,203],"extensive":[88],"entropy,":[90,129],"which":[91],"simply":[93],"subsystem":[98],"entropies.":[99],"In":[100],"contrast,":[101],"nonextensively":[106],"connected":[112],"through":[113],"long-range":[114],"interactions":[115],"that":[116,125,135,153,167],"produce":[117],"correlations.":[118],"defect":[124,134],"quantifies":[126,136],"missing":[128],"analogous":[130],"mass":[133,138],"(energy)":[139],"associated":[140],"assembling":[142],"subatomic":[143],"particles.":[144],"We":[145],"develop":[146],"connect":[154],"corresponding":[157],"kinetic":[158],"originated":[160],"Finally,":[164],"by":[174],"number":[176],"correlations,":[180],"determined":[182],"using":[183],"both":[184],"discrete":[185],"continuous":[187],"descriptions,":[188],"find:":[190],"(i)":[191],"resulted":[193],"entropic":[194],"form":[195],"expressed":[196],"terms":[198],"parameters;":[201],"(ii)":[202],"optimal":[204],"relationship":[205],"between":[206],"temperature;":[209],"(iii)":[211],"correlation":[213],"coefficient":[214],"be":[216],"inversely":[217],"proportional":[218],"logarithm.":[222]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":11},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":3}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2025-10-10T00:00:00"}