{"id":"https://openalex.org/W4410894454","doi":"https://doi.org/10.3390/e27060586","title":"Entropy Maximization, Time Emergence, and Phase Transition","display_name":"Entropy Maximization, Time Emergence, and Phase Transition","publication_year":2025,"publication_date":"2025-05-30","ids":{"openalex":"https://openalex.org/W4410894454","doi":"https://doi.org/10.3390/e27060586","pmid":"https://pubmed.ncbi.nlm.nih.gov/40566173"},"language":"en","primary_location":{"id":"doi:10.3390/e27060586","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27060586","pdf_url":"https://www.mdpi.com/1099-4300/27/6/586/pdf?version=1748608304","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/1099-4300/27/6/586/pdf?version=1748608304","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068463429","display_name":"Jonathan D. H. Smith","orcid":"https://orcid.org/0000-0002-2075-0744"},"institutions":[{"id":"https://openalex.org/I173911158","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78","country_code":"US","type":"education","lineage":["https://openalex.org/I173911158"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jonathan Smith","raw_affiliation_strings":["Department of Mathematics, Iowa State University, 411 Morrill Rd., Ames, IA 50011, USA"],"raw_orcid":"https://orcid.org/0000-0002-2075-0744","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Iowa State University, 411 Morrill Rd., Ames, IA 50011, USA","institution_ids":["https://openalex.org/I173911158"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5068463429"],"corresponding_institution_ids":["https://openalex.org/I173911158"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09049966,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"27","issue":"6","first_page":"586","last_page":"586"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.996399998664856,"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":0.996399998664856,"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":0.9898999929428101,"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/T10044","display_name":"Protein Structure and Dynamics","score":0.9886999726295471,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.6190184354782104},{"id":"https://openalex.org/keywords/entropy-maximization","display_name":"Entropy maximization","score":0.5692276954650879},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.543041467666626},{"id":"https://openalex.org/keywords/phase-transition","display_name":"Phase transition","score":0.5136925578117371},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.466207355260849},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4307872951030731},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.33124756813049316},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.2993173599243164},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.22556385397911072},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.20814529061317444},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.19253507256507874}],"concepts":[{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.6190184354782104},{"id":"https://openalex.org/C127233936","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Entropy maximization","level":3,"score":0.5692276954650879},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.543041467666626},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.5136925578117371},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.466207355260849},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4307872951030731},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.33124756813049316},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.2993173599243164},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.22556385397911072},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.20814529061317444},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.19253507256507874}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e27060586","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27060586","pdf_url":"https://www.mdpi.com/1099-4300/27/6/586/pdf?version=1748608304","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:40566173","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/40566173","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:doaj.org/article:0290a1389405497cbe2e5a1f9405c4b0","is_oa":true,"landing_page_url":"https://doaj.org/article/0290a1389405497cbe2e5a1f9405c4b0","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 27, Iss 6, p 586 (2025)","raw_type":"article"},{"id":"pmh:oai:pubmedcentral.nih.gov:12192101","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/12192101","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"}],"best_oa_location":{"id":"doi:10.3390/e27060586","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27060586","pdf_url":"https://www.mdpi.com/1099-4300/27/6/586/pdf?version=1748608304","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":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4410894454.pdf","grobid_xml":"https://content.openalex.org/works/W4410894454.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W126362881","https://openalex.org/W1967944020","https://openalex.org/W2032558547","https://openalex.org/W2044334254","https://openalex.org/W2050249319","https://openalex.org/W2054545804","https://openalex.org/W2087895317","https://openalex.org/W2100359709","https://openalex.org/W2130926302","https://openalex.org/W2165732266","https://openalex.org/W2171838068","https://openalex.org/W3021846434","https://openalex.org/W4252028749","https://openalex.org/W4313450652","https://openalex.org/W4388395091","https://openalex.org/W6873168925"],"related_works":["https://openalex.org/W3102188974","https://openalex.org/W3004810941","https://openalex.org/W4287870705","https://openalex.org/W3199097846","https://openalex.org/W624081655","https://openalex.org/W2519545954","https://openalex.org/W2180033908","https://openalex.org/W2576492542","https://openalex.org/W1952656308","https://openalex.org/W2267645079"],"abstract_inverted_index":{"We":[0],"survey":[1],"developments":[2],"in":[3,130],"the":[4,11,27,33,36,56,76,82,101,140,160,172,175,186,198],"use":[5,138],"of":[6,35,78,103,139,146,159],"entropy":[7,31,173],"maximization":[8],"for":[9,171,197],"applying":[10],"Gibbs":[12],"Canonical":[13,141],"Ensemble":[14,142],"to":[15,30,68,88,99,182,193],"finite":[16,199],"situations.":[17],"Biological":[18],"insights":[19],"are":[20,111,121],"invoked":[21],"along":[22],"with":[23,64,94,133],"physical":[24,62],"considerations.":[25],"In":[26,105,123],"game-theoretic":[28],"approach":[29],"maximization,":[32,174],"interpretation":[34],"two":[37],"player":[38],"roles":[39],"as":[40,155],"predator":[41],"and":[42,47,97,114],"prey":[43],"provides":[44],"a":[45,124,134,156,164,194],"well-justified":[46],"symmetric":[48],"analysis.":[49],"The":[50,151],"main":[51],"focus":[52],"is":[53,71,91,189],"placed":[54],"on":[55,167],"Lagrange":[57,84,152],"multiplier":[58,153],"approach.":[59],"Using":[60],"natural":[61],"units":[63,96],"Planck's":[65],"constant":[66],"set":[67],"unity,":[69],"it":[70],"recognized":[72],"that":[73],"energy":[74,109],"has":[75],"dimensions":[77],"inverse":[79],"time.":[80],"Thus,":[81],"conjugate":[83],"multiplier,":[85],"traditionally":[86],"related":[87],"absolute":[89],"temperature,":[90],"now":[92],"taken":[93],"time":[95],"oriented":[98],"follow":[100],"Arrow":[102],"Time.":[104],"quantum":[106],"optics,":[107],"where":[108,127],"levels":[110],"bounded":[112],"above":[113],"below,":[115],"artificial":[116],"singularities":[117],"involving":[118],"negative":[119],"temperatures":[120],"eliminated.":[122],"biological":[125],"model":[126],"species":[128],"compete":[129],"an":[131,144,168],"environment":[132],"fixed":[135],"carrying":[136,187],"capacity,":[137],"solves":[143],"instance":[145],"Eigen's":[147],"phenomenological":[148],"rate":[149],"equations.":[150],"emerges":[154],"statistical":[157],"measure":[158],"ecological":[161],"age.":[162],"Adding":[163],"weak":[165],"inequality":[166],"order":[169],"parameter":[170],"phase":[176],"transition":[177],"from":[178],"initial":[179],"unconstrained":[180],"growth":[181,184],"constrained":[183],"at":[185],"capacity":[188],"described,":[190],"without":[191],"recourse":[192],"thermodynamic":[195],"limit":[196],"system.":[200]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}