{"id":"https://openalex.org/W3198291217","doi":"https://doi.org/10.3390/e25020350","title":"The Typical Set and Entropy in Stochastic Systems with Arbitrary Phase Space Growth","display_name":"The Typical Set and Entropy in Stochastic Systems with Arbitrary Phase Space Growth","publication_year":2023,"publication_date":"2023-02-14","ids":{"openalex":"https://openalex.org/W3198291217","doi":"https://doi.org/10.3390/e25020350","mag":"3198291217","pmid":"https://pubmed.ncbi.nlm.nih.gov/36832717"},"language":"en","primary_location":{"id":"doi:10.3390/e25020350","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25020350","pdf_url":"https://www.mdpi.com/1099-4300/25/2/350/pdf?version=1676368376","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/1099-4300/25/2/350/pdf?version=1676368376","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019906371","display_name":"Rudolf Hanel","orcid":"https://orcid.org/0000-0002-4045-9532"},"institutions":[{"id":"https://openalex.org/I4210112164","display_name":"Complexity Science Hub","ror":"https://ror.org/023dz9m50","country_code":"AT","type":"nonprofit","lineage":["https://openalex.org/I4210112164"]},{"id":"https://openalex.org/I76134821","display_name":"Medical University of Vienna","ror":"https://ror.org/05n3x4p02","country_code":"AT","type":"education","lineage":["https://openalex.org/I76134821"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Rudolf Hanel","raw_affiliation_strings":["Complexity Science Hub Vienna, Josefst\u00e4dter Strasse 39, 1080 Vienna, Austria","Section for Science of Complex Systems, Medical University of Vienna, Spitalgasse 23, 1090 Vienna, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Complexity Science Hub Vienna, Josefst\u00e4dter Strasse 39, 1080 Vienna, Austria","institution_ids":["https://openalex.org/I4210112164"]},{"raw_affiliation_string":"Section for Science of Complex Systems, Medical University of Vienna, Spitalgasse 23, 1090 Vienna, Austria","institution_ids":["https://openalex.org/I76134821"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025590875","display_name":"Bernat Corominas\u2010Murtra","orcid":"https://orcid.org/0000-0001-9806-5643"},"institutions":[{"id":"https://openalex.org/I15766117","display_name":"University of Graz","ror":"https://ror.org/01faaaf77","country_code":"AT","type":"education","lineage":["https://openalex.org/I15766117"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Bernat Corominas-Murtra","raw_affiliation_strings":["Institute of Biology, University of Graz, Holteigasse 6, 8010 Graz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Biology, University of Graz, Holteigasse 6, 8010 Graz, Austria","institution_ids":["https://openalex.org/I15766117"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5025590875"],"corresponding_institution_ids":["https://openalex.org/I15766117"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.3842,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.50217494,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"25","issue":"2","first_page":"350","last_page":"350"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9983999729156494,"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9983999729156494,"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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9944000244140625,"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"}},{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.993399977684021,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5337788462638855},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5243868231773376},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.49424365162849426},{"id":"https://openalex.org/keywords/observable","display_name":"Observable","score":0.4900320768356323},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4845499098300934},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4698654115200043},{"id":"https://openalex.org/keywords/phase-space","display_name":"Phase space","score":0.4669056534767151},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.457836389541626},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3514378070831299}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5337788462638855},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5243868231773376},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.49424365162849426},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.4900320768356323},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4845499098300934},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4698654115200043},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.4669056534767151},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.457836389541626},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3514378070831299},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e25020350","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25020350","pdf_url":"https://www.mdpi.com/1099-4300/25/2/350/pdf?version=1676368376","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:36832717","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/36832717","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:pubmedcentral.nih.gov:9954961","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/9954961","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC9954961/pdf/entropy-25-00350.pdf","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:f6f989e0f7b7402bacd3f51567bca115","is_oa":true,"landing_page_url":"https://doaj.org/article/f6f989e0f7b7402bacd3f51567bca115","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 25, Iss 2, p 350 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/25/2/350/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e25020350","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","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e25020350","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25020350","pdf_url":"https://www.mdpi.com/1099-4300/25/2/350/pdf?version=1676368376","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":[{"id":"https://openalex.org/F4320325582","display_name":"Karl-Franzens-Universit\u00e4t Graz","ror":"https://ror.org/01faaaf77"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3198291217.pdf","grobid_xml":"https://content.openalex.org/works/W3198291217.grobid-xml"},"referenced_works_count":73,"referenced_works":["https://openalex.org/W24821895","https://openalex.org/W1484033701","https://openalex.org/W1554956811","https://openalex.org/W1573820523","https://openalex.org/W1966940255","https://openalex.org/W1966992904","https://openalex.org/W1972382697","https://openalex.org/W1976649818","https://openalex.org/W1982244066","https://openalex.org/W1995875735","https://openalex.org/W2022393257","https://openalex.org/W2032893024","https://openalex.org/W2056215740","https://openalex.org/W2078669571","https://openalex.org/W2083743389","https://openalex.org/W2088048184","https://openalex.org/W2089114542","https://openalex.org/W2090777257","https://openalex.org/W2099111195","https://openalex.org/W2108947461","https://openalex.org/W2115468292","https://openalex.org/W2120062331","https://openalex.org/W2122864540","https://openalex.org/W2125673923","https://openalex.org/W2152986532","https://openalex.org/W2156609166","https://openalex.org/W2158219778","https://openalex.org/W2168822965","https://openalex.org/W2341623870","https://openalex.org/W2475226298","https://openalex.org/W2482879788","https://openalex.org/W2486932837","https://openalex.org/W2496122279","https://openalex.org/W2516989746","https://openalex.org/W2586206329","https://openalex.org/W2617800306","https://openalex.org/W2732671119","https://openalex.org/W2751862591","https://openalex.org/W2755154271","https://openalex.org/W2774075108","https://openalex.org/W2805534999","https://openalex.org/W2887427821","https://openalex.org/W2890660244","https://openalex.org/W2933504771","https://openalex.org/W2947284360","https://openalex.org/W2963247734","https://openalex.org/W2963304669","https://openalex.org/W2963629961","https://openalex.org/W2964197556","https://openalex.org/W2964213744","https://openalex.org/W2975783521","https://openalex.org/W2993993911","https://openalex.org/W2996304749","https://openalex.org/W3011478619","https://openalex.org/W3088290060","https://openalex.org/W3098263245","https://openalex.org/W3099448335","https://openalex.org/W3099678069","https://openalex.org/W3102419798","https://openalex.org/W3104509924","https://openalex.org/W3104822214","https://openalex.org/W3105002542","https://openalex.org/W3105166638","https://openalex.org/W3112943580","https://openalex.org/W3121301815","https://openalex.org/W3124955094","https://openalex.org/W3133081295","https://openalex.org/W3138339412","https://openalex.org/W4238786632","https://openalex.org/W4302969465","https://openalex.org/W6658911534","https://openalex.org/W6775794996","https://openalex.org/W6891894458"],"related_works":["https://openalex.org/W1994680671","https://openalex.org/W2002320543","https://openalex.org/W2000283393","https://openalex.org/W2150232912","https://openalex.org/W2889012151","https://openalex.org/W2061947244","https://openalex.org/W4321855183","https://openalex.org/W15793755","https://openalex.org/W2498340320","https://openalex.org/W2081531990"],"abstract_inverted_index":{"is":[0,102],"key":[1],"for":[2,7,73],"data":[3],"compression":[4],"strategies":[5],"and":[6,66],"the":[8,36,60,116,128],"emergence":[9,37,118],"of":[10,27,38,71,78,106,110,119,130],"robust":[11,120],"statistical":[12,42],"observables":[13],"in":[14,51,122],"macroscopic":[15],"physical":[16],"systems.":[17,138],"Standard":[18],"approaches":[19],"derive":[20],"its":[21,32],"existence":[22,129],"from":[23,68],"a":[24,44,74,103],"restricted":[25],"set":[26,62],"dynamical":[28],"constraints.":[29],"However,":[30],"given":[31],"central":[33],"role":[34],"underlying":[35],"stable,":[39],"almost":[40],"deterministic":[41],"patterns,":[43],"question":[45],"arises":[46],"whether":[47],"typical":[48,61,131],"sets":[49,132],"exist":[50],"much":[52,75],"more":[53],"general":[54,69],"scenarios.":[55],"We":[56,113],"demonstrate":[57],"here":[58],"that":[59,100,115],"can":[63],"be":[64],"defined":[65],"characterized":[67],"forms":[70],"entropy":[72],"wider":[76],"class":[77],"stochastic":[79,107,124],"processes":[80,87],"than":[81],"was":[82],"previously":[83],"thought.":[84],"This":[85],"includes":[86],"showing":[88],"arbitrary":[89],"path":[90],"dependence,":[91],"long":[92],"range":[93],"correlations":[94],"or":[95],"dynamic":[96],"sampling":[97],"spaces,":[98],"suggesting":[99],"typicality":[101],"generic":[104],"property":[105],"processes,":[108],"regardless":[109],"their":[111],"complexity.":[112],"argue":[114],"potential":[117],"properties":[121],"complex":[123],"systems":[125],"provided":[126],"by":[127],"has":[133],"special":[134],"relevance":[135],"to":[136],"biological":[137]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}
