{"id":"https://openalex.org/W1635286099","doi":"https://doi.org/10.3390/e24050706","title":"R\u00e9nyi Entropy and Free Energy","display_name":"R\u00e9nyi Entropy and Free Energy","publication_year":2022,"publication_date":"2022-05-16","ids":{"openalex":"https://openalex.org/W1635286099","doi":"https://doi.org/10.3390/e24050706","mag":"1635286099","pmid":"https://pubmed.ncbi.nlm.nih.gov/35626588"},"language":"en","primary_location":{"id":"doi:10.3390/e24050706","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24050706","pdf_url":"https://www.mdpi.com/1099-4300/24/5/706/pdf?version=1652688691","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","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/24/5/706/pdf?version=1652688691","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056752880","display_name":"John C. Baez","orcid":"https://orcid.org/0000-0002-0609-9836"},"institutions":[{"id":"https://openalex.org/I103635307","display_name":"University of California, Riverside","ror":"https://ror.org/03nawhv43","country_code":"US","type":"education","lineage":["https://openalex.org/I103635307"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"John C. Baez","raw_affiliation_strings":["Department of Mathematics, University of California, Riverside, CA 92507, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Riverside, CA 92507, USA","institution_ids":["https://openalex.org/I103635307"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5056752880"],"corresponding_institution_ids":["https://openalex.org/I103635307"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":3.6327,"has_fulltext":false,"cited_by_count":74,"citation_normalized_percentile":{"value":0.93575664,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"24","issue":"5","first_page":"706","last_page":"706"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9991000294685364,"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9991000294685364,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9976999759674072,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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":0.637234091758728},{"id":"https://openalex.org/keywords/joint-quantum-entropy","display_name":"Joint quantum entropy","score":0.5488853454589844},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5458146333694458},{"id":"https://openalex.org/keywords/entropy-in-thermodynamics-and-information-theory","display_name":"Entropy in thermodynamics and information theory","score":0.4966180920600891},{"id":"https://openalex.org/keywords/r\u00e9nyi-entropy","display_name":"R\u00e9nyi entropy","score":0.4641372561454773},{"id":"https://openalex.org/keywords/second-law-of-thermodynamics","display_name":"Second law of thermodynamics","score":0.45910099148750305},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4507933259010315},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.432686448097229},{"id":"https://openalex.org/keywords/maximum-entropy-thermodynamics","display_name":"Maximum entropy thermodynamics","score":0.4092302620410919},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.4041443169116974},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3694879412651062},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.2684176564216614},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.19034349918365479},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.071932852268219}],"concepts":[{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.637234091758728},{"id":"https://openalex.org/C42047476","wikidata":"https://www.wikidata.org/wiki/Q6269544","display_name":"Joint quantum entropy","level":3,"score":0.5488853454589844},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5458146333694458},{"id":"https://openalex.org/C148563202","wikidata":"https://www.wikidata.org/wiki/Q5380803","display_name":"Entropy in thermodynamics and information theory","level":5,"score":0.4966180920600891},{"id":"https://openalex.org/C142611142","wikidata":"https://www.wikidata.org/wiki/Q1433083","display_name":"R\u00e9nyi entropy","level":3,"score":0.4641372561454773},{"id":"https://openalex.org/C119820323","wikidata":"https://www.wikidata.org/wiki/Q177045","display_name":"Second law of thermodynamics","level":2,"score":0.45910099148750305},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4507933259010315},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.432686448097229},{"id":"https://openalex.org/C49775889","wikidata":"https://www.wikidata.org/wiki/Q6795896","display_name":"Maximum entropy thermodynamics","level":4,"score":0.4092302620410919},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4041443169116974},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3694879412651062},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.2684176564216614},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.19034349918365479},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.071932852268219}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.3390/e24050706","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24050706","pdf_url":"https://www.mdpi.com/1099-4300/24/5/706/pdf?version=1652688691","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:35626588","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/35626588","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:arXiv.org:1102.2098","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1102.2098","pdf_url":"https://arxiv.org/pdf/1102.2098","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:CiteSeerX.psu:10.1.1.745.4300","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.745.4300","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1102.2098.pdf","raw_type":"text"},{"id":"pmh:oai:doaj.org/article:705ab928376e4edebd6bccbc6ed87e84","is_oa":true,"landing_page_url":"https://doaj.org/article/705ab928376e4edebd6bccbc6ed87e84","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 24, Iss 5, p 706 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/24/5/706/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e24050706","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 24; Issue 5; Pages: 706","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:9140207","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/9140207","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","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":"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"}],"best_oa_location":{"id":"doi:10.3390/e24050706","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24050706","pdf_url":"https://www.mdpi.com/1099-4300/24/5/706/pdf?version=1652688691","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":0.8700000047683716,"id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1635286099.pdf","grobid_xml":"https://content.openalex.org/works/W1635286099.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W110288970","https://openalex.org/W1485301842","https://openalex.org/W1553236419","https://openalex.org/W1635286099","https://openalex.org/W1970412632","https://openalex.org/W2034773169","https://openalex.org/W2083682556","https://openalex.org/W2094545983","https://openalex.org/W2164253138","https://openalex.org/W3102270073","https://openalex.org/W4230367971","https://openalex.org/W6636650941"],"related_works":["https://openalex.org/W2043360696","https://openalex.org/W2970357377","https://openalex.org/W2300741437","https://openalex.org/W1991851767","https://openalex.org/W2182029627","https://openalex.org/W3114186922","https://openalex.org/W4247532445","https://openalex.org/W2530050266","https://openalex.org/W2944647124","https://openalex.org/W4253578787"],"abstract_inverted_index":{"The":[0],"R\u00e9nyi":[1,20,73,97,121],"entropy":[2,11,21,74,98,122],"is":[3,22,105,123],"a":[4,15,32,100,124],"generalization":[5],"of":[6,10,49,99,109,126,130],"the":[7,41,46,51,61,66,71,96,107,116,127],"usual":[8,128],"concept":[9,129],"which":[12],"depends":[13],"on":[14],"parameter":[16],"<i>q</i>.":[17,44],"In":[18],"fact,":[19],"closely":[23],"related":[24],"to":[25,58,82,115],"free":[26,111],"energy.":[27],"Suppose":[28],"we":[29,89],"start":[30],"with":[31,113],"system":[33,52,101],"in":[34,68,75,102],"thermal":[35,103],"equilibrium":[36,59,104],"and":[37,85],"then":[38],"suddenly":[39],"divide":[40],"temperature":[42,63,69],"by":[43,65],"Then":[45],"maximum":[47],"amount":[48],"work":[50],"can":[53,90],"perform":[54],"as":[55,94],"it":[56],"moves":[57],"at":[60],"new":[62],"divided":[64],"change":[67],"equals":[70],"system's":[72],"its":[76,110],"original":[77],"state.":[78],"This":[79,118],"result":[80,93],"applies":[81],"both":[83],"classical":[84],"quantum":[86],"systems.":[87],"Mathematically,":[88],"express":[91],"this":[92],"follows:":[95],"without":[106],"'q-1-derivative'":[108],"energy":[112],"respect":[114],"temperature.":[117],"shows":[119],"that":[120],"<i>q</i>-deformation":[125],"entropy.":[131]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
