{"id":"https://openalex.org/W3204511977","doi":null,"title":"A Notion of Entropy for Stochastic Processes","display_name":"A Notion of Entropy for Stochastic Processes","publication_year":2021,"publication_date":"2021-10-04","ids":{"openalex":"https://openalex.org/W3204511977","mag":"3204511977"},"language":"en","primary_location":{"id":"mag:3204511977","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2110.01541","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2110.01541","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043781888","display_name":"Maysam Maysami Sadr","orcid":"https://orcid.org/0000-0003-0747-4180","observed_orcids":["https://orcid.org/0000-0003-0747-4180"]},"institutions":[{"id":"https://openalex.org/I161028277","display_name":"Institute for Advanced Studies in Basic Sciences","ror":"https://ror.org/00bzsst90","country_code":"IR","type":"education","lineage":["https://openalex.org/I161028277"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Maysam Maysami Sadr","raw_affiliation_strings":["Institute for Advanced Studies in Basic Sciences"],"raw_orcid":"https://orcid.org/0000-0003-0747-4180","affiliations":[{"raw_affiliation_string":"Institute for Advanced Studies in Basic Sciences","institution_ids":["https://openalex.org/I161028277"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027677905","display_name":"Mina Shahrestani","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I161028277","display_name":"Institute for Advanced Studies in Basic Sciences","ror":"https://ror.org/00bzsst90","country_code":"IR","type":"education","lineage":["https://openalex.org/I161028277"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Mina Shahrestani","raw_affiliation_strings":["Institute for Advanced Studies in Basic Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Advanced Studies in Basic Sciences","institution_ids":["https://openalex.org/I161028277"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I161028277"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13234","display_name":"p-Adic Analysis and Mathematical Physics","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/dynamical-entropy","display_name":"dynamical entropy","score":0.9829999804496765},{"id":"https://openalex.org/keywords/discrete-time-stochastic-processes","display_name":"discrete-time stochastic processes","score":0.8600000143051147},{"id":"https://openalex.org/keywords/measure-preserving-transformations","display_name":"measure-preserving transformations","score":0.871999979019165},{"id":"https://openalex.org/keywords/stationary-processes","display_name":"stationary processes","score":0.9390000104904175},{"id":"https://openalex.org/keywords/shift-transformation","display_name":"shift transformation","score":0.7649999856948853},{"id":"https://openalex.org/keywords/path-space","display_name":"path space","score":0.9279999732971191},{"id":"https://openalex.org/keywords/topological-entropy","display_name":"topological entropy","score":0.9350000023841858},{"id":"https://openalex.org/keywords/variational-inequalities","display_name":"variational inequalities","score":0.9760000109672546}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7749656438827515},{"id":"https://openalex.org/C125252325","wikidata":"https://www.wikidata.org/wiki/Q1345213","display_name":"Entropy rate","level":4,"score":0.6770039200782776},{"id":"https://openalex.org/C42047476","wikidata":"https://www.wikidata.org/wiki/Q6269544","display_name":"Joint quantum entropy","level":3,"score":0.5808324813842773},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5586919188499451},{"id":"https://openalex.org/C5084201","wikidata":"https://www.wikidata.org/wiki/Q17090689","display_name":"Generalized relative entropy","level":5,"score":0.5098444819450378},{"id":"https://openalex.org/C2780350623","wikidata":"https://www.wikidata.org/wiki/Q3055355","display_name":"Topological entropy","level":2,"score":0.5056779384613037},{"id":"https://openalex.org/C49775889","wikidata":"https://www.wikidata.org/wiki/Q6795896","display_name":"Maximum entropy thermodynamics","level":4,"score":0.4954761266708374},{"id":"https://openalex.org/C60507348","wikidata":"https://www.wikidata.org/wiki/Q6795892","display_name":"Maximum entropy probability distribution","level":3,"score":0.45335403084754944},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4421161413192749},{"id":"https://openalex.org/C24495805","wikidata":"https://www.wikidata.org/wiki/Q7269091","display_name":"Quantum relative entropy","level":5,"score":0.42636173963546753},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.4148562550544739},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37096014618873596},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3700110912322998},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.28976958990097046},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10843402147293091},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06531479954719543},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.059501707553863525},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.0},{"id":"https://openalex.org/C139356082","wikidata":"https://www.wikidata.org/wiki/Q7269038","display_name":"Quantum discord","level":4,"score":0.0},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:3204511977","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2110.01541","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"mag:3204511977","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2110.01541","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4286911639","https://openalex.org/W1989075956","https://openalex.org/W2041933359","https://openalex.org/W3020991580","https://openalex.org/W2735402264","https://openalex.org/W2213247601","https://openalex.org/W2278757289","https://openalex.org/W4392781013","https://openalex.org/W2413221132","https://openalex.org/W1998788396"],"abstract_inverted_index":{"A":[0,75],"notion":[1,72],"of":[2,23,30,38,49,57,70,81,84],"dynamical":[3],"entropy":[4,22,37,48,56,80],"for":[5,78],"discrete-time":[6],"stochastic":[7,25],"processes":[8],"with":[9,35,54],"values":[10],"in":[11],"arbitrary":[12,82],"measurable":[13],"spaces":[14,87],"is":[15,44,88],"introduced.":[16],"It":[17],"turns":[18],"out":[19],"that":[20,46],"the":[21,24,39,47,61,65],"process":[26,52],"defined":[27],"by":[28],"iterations":[29],"a":[31],"measure-preserving":[32],"transformation":[33,59],"coincides":[34,53],"(ordinary)":[36,55],"transformation.":[40],"More":[41],"generally,":[42],"it":[43],"shown":[45],"any":[50],"stationary":[51],"shift":[58],"on":[60],"path-space":[62],"associated":[63],"to":[64],"process.":[66],"Various":[67],"basic":[68],"properties":[69],"this":[71],"are":[73],"considered.":[74],"variational":[76],"inequality":[77],"topological":[79],"subsets":[83],"infinite":[85],"product":[86],"given.":[89]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2021-10-11T00:00:00"}
