{"id":"https://openalex.org/W2105396835","doi":"https://doi.org/10.3390/e16010001","title":"Entropy and Equilibria in Competitive Systems","display_name":"Entropy and Equilibria in Competitive Systems","publication_year":2013,"publication_date":"2013-12-24","ids":{"openalex":"https://openalex.org/W2105396835","doi":"https://doi.org/10.3390/e16010001","mag":"2105396835"},"language":"en","primary_location":{"id":"doi:10.3390/e16010001","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e16010001","pdf_url":"https://www.mdpi.com/1099-4300/16/1/1/pdf?version=1424785197","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":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/16/1/1/pdf?version=1424785197","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001527588","display_name":"A. Klimenko","orcid":"https://orcid.org/0000-0003-4255-9374"},"institutions":[{"id":"https://openalex.org/I165143802","display_name":"The University of Queensland","ror":"https://ror.org/00rqy9422","country_code":"AU","type":"education","lineage":["https://openalex.org/I165143802"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"A. Klimenko","raw_affiliation_strings":["The University of Queensland, SoMME, QLD 4072, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The University of Queensland, SoMME, QLD 4072, Australia","institution_ids":["https://openalex.org/I165143802"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5001527588"],"corresponding_institution_ids":["https://openalex.org/I165143802"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":1.1434,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.78614027,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"16","issue":"1","first_page":"1","last_page":"22"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9986000061035156,"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":0.9986000061035156,"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9799000024795532,"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":0.9749000072479248,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/punctuated-equilibrium","display_name":"Punctuated equilibrium","score":0.7849248647689819},{"id":"https://openalex.org/keywords/transitive-relation","display_name":"Transitive relation","score":0.6583235263824463},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.516781210899353},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4938822388648987},{"id":"https://openalex.org/keywords/competition","display_name":"Competition (biology)","score":0.4710271954536438},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.45851799845695496},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4474204480648041},{"id":"https://openalex.org/keywords/evolving-systems","display_name":"Evolving systems","score":0.44385772943496704},{"id":"https://openalex.org/keywords/dilemma","display_name":"Dilemma","score":0.44372305274009705},{"id":"https://openalex.org/keywords/thermodynamic-system","display_name":"Thermodynamic system","score":0.41952022910118103},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.40264856815338135},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3424699604511261},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.2662309408187866},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.1905824840068817},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17294296622276306},{"id":"https://openalex.org/keywords/management-science","display_name":"Management science","score":0.1464197337627411},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.13088923692703247},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.08704429864883423},{"id":"https://openalex.org/keywords/evolutionary-biology","display_name":"Evolutionary biology","score":0.0775446891784668}],"concepts":[{"id":"https://openalex.org/C148108004","wikidata":"https://www.wikidata.org/wiki/Q582558","display_name":"Punctuated equilibrium","level":2,"score":0.7849248647689819},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.6583235263824463},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.516781210899353},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4938822388648987},{"id":"https://openalex.org/C91306197","wikidata":"https://www.wikidata.org/wiki/Q45767","display_name":"Competition (biology)","level":2,"score":0.4710271954536438},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.45851799845695496},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4474204480648041},{"id":"https://openalex.org/C2988305597","wikidata":"https://www.wikidata.org/wiki/Q215772","display_name":"Evolving systems","level":2,"score":0.44385772943496704},{"id":"https://openalex.org/C2778496695","wikidata":"https://www.wikidata.org/wiki/Q254128","display_name":"Dilemma","level":2,"score":0.44372305274009705},{"id":"https://openalex.org/C14380042","wikidata":"https://www.wikidata.org/wiki/Q503327","display_name":"Thermodynamic system","level":2,"score":0.41952022910118103},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.40264856815338135},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3424699604511261},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.2662309408187866},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.1905824840068817},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17294296622276306},{"id":"https://openalex.org/C539667460","wikidata":"https://www.wikidata.org/wiki/Q2414942","display_name":"Management science","level":1,"score":0.1464197337627411},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.13088923692703247},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.08704429864883423},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0775446891784668},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e16010001","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e16010001","pdf_url":"https://www.mdpi.com/1099-4300/16/1/1/pdf?version=1424785197","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":"pmh:oai:arXiv.org:1403.1793","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1403.1793","pdf_url":"https://arxiv.org/pdf/1403.1793","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:eba6f91c64e74137b0b4e85a327700de","is_oa":true,"landing_page_url":"https://doaj.org/article/eba6f91c64e74137b0b4e85a327700de","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 16, Iss 1, Pp 1-22 (2013)","raw_type":"article"},{"id":"pmh:oai:espace.library.uq.edu.au:UQ:323417","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306402388","display_name":"Queensland's institutional digital repository (The University of Queensland)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I165143802","host_organization_name":"The University of Queensland","host_organization_lineage":["https://openalex.org/I165143802"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:oai:mdpi.com:/1099-4300/16/1/1/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e16010001","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; Volume 16; Issue 1; Pages: 1-22","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e16010001","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e16010001","pdf_url":"https://www.mdpi.com/1099-4300/16/1/1/pdf?version=1424785197","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W168346993","https://openalex.org/W1551940242","https://openalex.org/W1564500292","https://openalex.org/W1967716899","https://openalex.org/W1984497030","https://openalex.org/W1986404331","https://openalex.org/W2004006453","https://openalex.org/W2009185635","https://openalex.org/W2012813817","https://openalex.org/W2056971998","https://openalex.org/W2085947407","https://openalex.org/W2088048184","https://openalex.org/W2089852843","https://openalex.org/W2093042238","https://openalex.org/W2131390503","https://openalex.org/W2135030422","https://openalex.org/W2166660798","https://openalex.org/W2166697697","https://openalex.org/W3100432100","https://openalex.org/W3100722022","https://openalex.org/W3100749287","https://openalex.org/W3104822214"],"related_works":["https://openalex.org/W2161392352","https://openalex.org/W3210797322","https://openalex.org/W3214584237","https://openalex.org/W2090196252","https://openalex.org/W4388228191","https://openalex.org/W154453556","https://openalex.org/W1979284649","https://openalex.org/W2149441121","https://openalex.org/W2105396835","https://openalex.org/W3200884092"],"abstract_inverted_index":{"This":[0,66],"paper":[1],"investigates":[2],"the":[3,21,58,61,69,75,78],"applicability":[4],"of":[5,23,36,60,71,77],"thermodynamic":[6,53],"concepts":[7],"and":[8,43,50,57],"principles":[9],"to":[10],"competitive":[11,39,79],"systems.":[12],"We":[13],"show":[14],"that":[15],"Tsallis":[16],"entropies":[17],"are":[18,41,55],"suitable":[19],"for":[20],"characterisation":[22],"systems":[24,40],"with":[25],"transitive":[26],"competition":[27,46],"when":[28],"mutations":[29],"deviate":[30],"from":[31],"Gibbs":[32],"mutations.":[33],"Different":[34],"types":[35],"equilibria":[37],"in":[38,74],"considered":[42],"analysed.":[44],"As":[45],"rules":[47],"become":[48,64],"more":[49,51],"intransitive,":[52],"analogies":[54],"eroded,":[56],"behaviour":[59],"system":[62],"can":[63],"complex.":[65],"work":[67],"analyses":[68],"phenomenon":[70],"punctuated":[72],"evolution":[73],"context":[76],"risk/benefit":[80],"dilemma.":[81]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
