{"id":"https://openalex.org/W4402190982","doi":"https://doi.org/10.3390/e28060654","title":"Expectation Identities for Dynamical Systems: A Classical Analog of the Ehrenfest Theorem","display_name":"Expectation Identities for Dynamical Systems: A Classical Analog of the Ehrenfest Theorem","publication_year":2026,"publication_date":"2026-06-09","ids":{"openalex":"https://openalex.org/W4402190982","doi":"https://doi.org/10.3390/e28060654","pmid":"https://pubmed.ncbi.nlm.nih.gov/42352163"},"language":"en","primary_location":{"id":"doi:10.3390/e28060654","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28060654","pdf_url":null,"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://doi.org/10.3390/e28060654","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089117168","display_name":"Abiam Tamburrini","orcid":"https://orcid.org/0000-0001-7633-2739"},"institutions":[{"id":"https://openalex.org/I69737025","display_name":"University of Chile","ror":"https://ror.org/047gc3g35","country_code":"CL","type":"education","lineage":["https://openalex.org/I69737025"]}],"countries":["CL"],"is_corresponding":true,"raw_author_name":"Abiam Tamburrini","raw_affiliation_strings":["University of Chile","University of Chile, Chile"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Chile","institution_ids":["https://openalex.org/I69737025"]},{"raw_affiliation_string":"University of Chile, Chile","institution_ids":["https://openalex.org/I69737025"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009958523","display_name":"Sergio Davis","orcid":"https://orcid.org/0000-0003-2757-332X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sergio Davis","raw_affiliation_strings":["Independent  - affiliation not provided to SSRN"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Independent  - affiliation not provided to SSRN","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100737992","display_name":"Diego Luis Gonzalez","orcid":"https://orcid.org/0000-0001-9646-9900"},"institutions":[{"id":"https://openalex.org/I2802166871","display_name":"Universidad Cat\u00f3lica del Norte","ror":"https://ror.org/02akpm128","country_code":"CL","type":"education","lineage":["https://openalex.org/I2802166871"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"Diego Gonz\u00e1lez","raw_affiliation_strings":["Universidad Catolica del Norte","Universidad Catolica del Norte, Avda Angamos 0610, Antofagasta, Chile"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidad Catolica del Norte","institution_ids":["https://openalex.org/I2802166871"]},{"raw_affiliation_string":"Universidad Catolica del Norte, Avda Angamos 0610, Antofagasta, Chile","institution_ids":["https://openalex.org/I2802166871"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049791932","display_name":"Pablo S. Moya","orcid":"https://orcid.org/0000-0002-9161-0888"},"institutions":[{"id":"https://openalex.org/I69737025","display_name":"University of Chile","ror":"https://ror.org/047gc3g35","country_code":"CL","type":"education","lineage":["https://openalex.org/I69737025"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"Pablo  S. Moya","raw_affiliation_strings":["University of Chile","University of Chile, Chile"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Chile","institution_ids":["https://openalex.org/I69737025"]},{"raw_affiliation_string":"University of Chile, Chile","institution_ids":["https://openalex.org/I69737025"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5089117168"],"corresponding_institution_ids":["https://openalex.org/I69737025"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0040839,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":"6","first_page":"654","last_page":"654"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9272000193595886,"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"}},"topics":[{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9272000193595886,"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"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9226999878883362,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5181894898414612},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5069472789764404},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.39936524629592896},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36938661336898804},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3635116219520569},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3501681089401245},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.33762311935424805},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.19045156240463257}],"concepts":[{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5181894898414612},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5069472789764404},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.39936524629592896},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36938661336898804},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3635116219520569},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3501681089401245},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.33762311935424805},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.19045156240463257}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e28060654","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28060654","pdf_url":null,"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":"doi:10.2139/ssrn.4944473","is_oa":true,"landing_page_url":"http://dx.doi.org/10.2139/ssrn.4944473","pdf_url":null,"source":{"id":"https://openalex.org/S4210172589","display_name":"SSRN Electronic Journal","issn_l":"1556-5068","issn":["1556-5068"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1318003438","host_organization_name":"RELX Group (Netherlands)","host_organization_lineage":["https://openalex.org/I1318003438"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"},{"id":"pmid:42352163","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/42352163","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":"Journal Article"},{"id":"pmh:oai:doaj.org/article:650d664c73b64c19b54d1983b4b94487","is_oa":false,"landing_page_url":"https://doaj.org/article/650d664c73b64c19b54d1983b4b94487","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 28, Iss 6, p 654 (2026)","raw_type":"article"},{"id":"pmh:oai:pubmedcentral.nih.gov:13298719","is_oa":true,"landing_page_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC13298719/","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/e28060654","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28060654","pdf_url":null,"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":[{"id":"https://openalex.org/G4371037697","display_name":null,"funder_award_id":"21210407","funder_id":"https://openalex.org/F4320331146","funder_display_name":"Agencia Nacional de Investigaci\u00f3n y Desarrollo"}],"funders":[{"id":"https://openalex.org/F4320331146","display_name":"Agencia Nacional de Investigaci\u00f3n y Desarrollo","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1498924426","https://openalex.org/W1528941559","https://openalex.org/W2004566760","https://openalex.org/W2036157844","https://openalex.org/W2043785977","https://openalex.org/W2058703660","https://openalex.org/W2076602648","https://openalex.org/W2080993911","https://openalex.org/W2084380097","https://openalex.org/W2087703210","https://openalex.org/W2172479319","https://openalex.org/W2271959286","https://openalex.org/W2344888408","https://openalex.org/W2480136563","https://openalex.org/W2811360219","https://openalex.org/W3125432560","https://openalex.org/W4240788980","https://openalex.org/W4299551239","https://openalex.org/W4388167314","https://openalex.org/W4388795797"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2230606337","https://openalex.org/W2330535098","https://openalex.org/W1541871911","https://openalex.org/W140420611","https://openalex.org/W4250831671","https://openalex.org/W847258906","https://openalex.org/W2541737411","https://openalex.org/W2116135673","https://openalex.org/W2287528599"],"abstract_inverted_index":{"In":[0,143],"this":[1],"work,":[2],"we":[3,145],"formulate":[4],"a":[5,69,103,153,167],"systematic":[6,154],"expectation-value":[7],"framework":[8,106,138],"for":[9,53,73,107,157,171],"dynamical":[10],"systems":[11,158],"whose":[12],"probability":[13],"densities":[14],"evolve":[15],"according":[16],"to":[17],"linear":[18,79,161],"partial":[19],"differential":[20],"equations,":[21,163],"such":[22],"as":[23,152,166],"the":[24,38,42,47,61,83,100,119,130,137,148],"Fokker-Planck":[25,124],"and":[26,41,56,76,125,128,133],"Liouville":[27,126],"equations.":[28],"The":[29,65],"approach":[30],"is":[31,150],"based":[32],"on":[33],"expectation-calculus":[34],"identities":[35],"associated":[36],"with":[37,121],"Fluctuation-Dissipation":[39],"Theorem":[40],"Conjugate":[43],"Variables":[44],"Theorem,":[45],"allowing":[46],"derivation":[48],"of":[49,136],"evolution":[50,162],"equations":[51,85],"directly":[52],"arbitrary":[54,172],"observables":[55],"fluctuations":[57,77],"without":[58],"explicitly":[59],"solving":[60],"full":[62],"probability-density":[63,80],"equation.":[64],"resulting":[66,84],"relations":[67],"provide":[68],"classical":[70],"Ehrenfest-type":[71],"formulation":[72,156],"observable":[74,109],"dynamics":[75,110,127],"under":[78,111],"evolution.":[81],"While":[82],"are":[86],"not":[87],"closed":[88],"in":[89,139],"general,":[90],"since":[91],"they":[92],"typically":[93],"involve":[94],"higher-order":[95],"moments,":[96],"correlations,":[97],"or":[98,114],"derivatives,":[99],"formalism":[101],"offers":[102],"unified":[104],"operational":[105],"studying":[108],"suitable":[112],"approximations":[113],"closure":[115,169],"assumptions.":[116],"We":[117],"illustrate":[118],"procedure":[120],"examples":[122],"involving":[123],"discuss":[129],"scope,":[131],"limitations,":[132],"possible":[134],"applications":[135],"nonequilibrium":[140,173],"statistical":[141],"mechanics.":[142],"particular,":[144],"emphasize":[146],"that":[147],"method":[149],"intended":[151],"observable-based":[155],"governed":[159],"by":[160],"rather":[164],"than":[165],"universal":[168],"scheme":[170],"dynamics.":[174]},"counts_by_year":[],"updated_date":"2026-08-04T08:18:43.703281","created_date":"2025-10-10T00:00:00"}
