{"id":"https://openalex.org/W7214211849","doi":"https://doi.org/10.48550/arxiv.2609.27705","title":"Multiscale Entropies as Order Parameters for Nonequilibrium Phase Transitions","display_name":"Multiscale Entropies as Order Parameters for Nonequilibrium Phase Transitions","publication_year":2026,"publication_date":"2026-09-23","ids":{"openalex":"https://openalex.org/W7214211849","doi":"https://doi.org/10.48550/arxiv.2609.27705"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.27705","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.27705","pdf_url":"https://arxiv.org/pdf/2609.27705","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.27705","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025435542","display_name":"Gerhard Jung","orcid":"https://orcid.org/0000-0002-6739-1603","observed_orcids":["https://orcid.org/0000-0002-6739-1603"]},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Jung, Gerhard","raw_affiliation_strings":["Institut f\u00fcr Theoretische Physik , Universit\u00e4t Innsbruck , 6020 Innsbruck , Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Theoretische Physik , Universit\u00e4t Innsbruck , 6020 Innsbruck , Austria","institution_ids":["https://openalex.org/I190249584"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022051801","display_name":"Misaki Ozawa","orcid":"https://orcid.org/0000-0002-4603-8878","observed_orcids":["https://orcid.org/0000-0002-4603-8878"]},"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/I4210113150","display_name":"Laboratoire Interdisciplinaire de Physique","ror":"https://ror.org/023n9q531","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4210113150","https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Ozawa, Misaki","raw_affiliation_strings":["Univ. Grenoble Alpes , CNRS , LIPhy , 38000 Grenoble , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ. Grenoble Alpes , CNRS , LIPhy , 38000 Grenoble , France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210113150"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.9746000170707703,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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/T10591","display_name":"Theoretical and Computational Physics","score":0.9746000170707703,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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":0.008500000461935997,"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":0.0038999998942017555,"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/multiscale-entropy","display_name":"multiscale entropy","score":0.9980000257492065},{"id":"https://openalex.org/keywords/shannon-entropy","display_name":"Shannon entropy","score":0.777999997138977},{"id":"https://openalex.org/keywords/order-parameter","display_name":"order parameter","score":0.753000020980835},{"id":"https://openalex.org/keywords/nonequilibrium-phase-transitions","display_name":"nonequilibrium phase transitions","score":0.9990000128746033},{"id":"https://openalex.org/keywords/criticality","display_name":"criticality","score":0.6830000281333923},{"id":"https://openalex.org/keywords/phi-4-theory","display_name":"phi^4 theory","score":0.9789999723434448},{"id":"https://openalex.org/keywords/pattern-formation","display_name":"pattern formation","score":0.8199999928474426},{"id":"https://openalex.org/keywords/generative-models","display_name":"generative models","score":0.7490000128746033},{"id":"https://openalex.org/keywords/spatial-organization","display_name":"spatial organization","score":0.5299999713897705}],"concepts":[{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.8317000269889832},{"id":"https://openalex.org/C74859849","wikidata":"https://www.wikidata.org/wiki/Q2466686","display_name":"Non-equilibrium thermodynamics","level":2,"score":0.820900022983551},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.6043999791145325},{"id":"https://openalex.org/C68532491","wikidata":"https://www.wikidata.org/wiki/Q1203669","display_name":"Renormalization group","level":2,"score":0.5701000094413757},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5526999831199646},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.4959000051021576},{"id":"https://openalex.org/C125611927","wikidata":"https://www.wikidata.org/wiki/Q17008131","display_name":"Criticality","level":2,"score":0.49309998750686646},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4618000090122223},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38530001044273376},{"id":"https://openalex.org/C133905733","wikidata":"https://www.wikidata.org/wiki/Q2629238","display_name":"Multifractal system","level":3,"score":0.3619999885559082},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.3458999991416931},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.3452000021934509},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.3440000116825104},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.2955999970436096},{"id":"https://openalex.org/C99874945","wikidata":"https://www.wikidata.org/wiki/Q188715","display_name":"Statistical mechanics","level":2,"score":0.2906999886035919},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.2782999873161316},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.27489998936653137},{"id":"https://openalex.org/C44492722","wikidata":"https://www.wikidata.org/wiki/Q327069","display_name":"Conditional probability","level":2,"score":0.2743000090122223},{"id":"https://openalex.org/C201779956","wikidata":"https://www.wikidata.org/wiki/Q5426803","display_name":"Ergodicity","level":2,"score":0.27149999141693115},{"id":"https://openalex.org/C49775889","wikidata":"https://www.wikidata.org/wiki/Q6795896","display_name":"Maximum entropy thermodynamics","level":4,"score":0.26980000734329224},{"id":"https://openalex.org/C75438885","wikidata":"https://www.wikidata.org/wiki/Q3403615","display_name":"Large deviations theory","level":2,"score":0.25769999623298645},{"id":"https://openalex.org/C166124518","wikidata":"https://www.wikidata.org/wiki/Q1047702","display_name":"Renormalization","level":2,"score":0.2558000087738037},{"id":"https://openalex.org/C26546657","wikidata":"https://www.wikidata.org/wiki/Q1412452","display_name":"Fractal dimension","level":3,"score":0.2540000081062317}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.27705","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.27705","pdf_url":"https://arxiv.org/pdf/2609.27705","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2609.27705","doi":"https://doi.org/10.48550/arxiv.2609.27705","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.27705","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.27705","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.27705","pdf_url":"https://arxiv.org/pdf/2609.27705","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1081205762","display_name":"Modeling and Exploiting Non-Equilibrium Soft Matter","funder_award_id":"PAT1139125","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G5243951089","display_name":"MIAI Cluster","funder_award_id":"ANR-23-IACL-0006","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7080048889","display_name":null,"funder_award_id":"ANR-23","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214211849.pdf","grobid_xml":"https://content.openalex.org/works/W7214211849.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W4396816535","https://openalex.org/W7148251470","https://openalex.org/W7162770685","https://openalex.org/W7204963655","https://openalex.org/W7212072360"],"related_works":["https://openalex.org/W7098206278","https://openalex.org/W2146906211","https://openalex.org/W7096312007","https://openalex.org/W7117790909","https://openalex.org/W7163892641","https://openalex.org/W7118186872","https://openalex.org/W2009304932","https://openalex.org/W4224863237","https://openalex.org/W3198411702","https://openalex.org/W7100353602"],"abstract_inverted_index":{"We":[0],"develop":[1],"a":[2],"multiscale":[3,60],"entropy":[4,18],"framework":[5],"based":[6],"on":[7],"the":[8,15,49,69],"wavelet":[9],"conditional":[10],"renormalization":[11],"group":[12],"that":[13,59],"decomposes":[14],"total":[16,70],"Shannon":[17],"into":[19],"contributions":[20],"from":[21,33],"different":[22],"spatial":[23,65],"scales.":[24],"Generative":[25],"modeling":[26],"enables":[27],"accurate":[28],"estimation":[29],"of":[30],"these":[31],"entropies":[32,61,73],"configurations":[34],"or":[35],"snapshots,":[36],"even":[37],"in":[38,68],"nonequilibrium":[39,54],"systems":[40],"whose":[41],"underlying":[42],"probability":[43],"distributions":[44],"are":[45],"unknown.":[46],"Applications":[47],"to":[48],"equilibrium":[50],"$\u03c6^4$":[51],"model":[52],"and":[53,64,83],"active":[55],"Model":[56],"B+":[57],"show":[58],"reveal":[62],"criticality":[63],"organization":[66],"obscured":[67],"entropy.":[71],"These":[72],"serve":[74],"as":[75],"scale-dependent":[76],"order":[77],"parameters":[78],"for":[79],"characterizing":[80],"phase":[81],"transitions":[82],"pattern":[84],"formation.":[85]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-25T00:00:00"}