{"id":"https://openalex.org/W2062843442","doi":"https://doi.org/10.1109/tit.2014.2357799","title":"On the Conditional R\u00e9nyi Entropy","display_name":"On the Conditional R\u00e9nyi Entropy","publication_year":2014,"publication_date":"2014-09-12","ids":{"openalex":"https://openalex.org/W2062843442","doi":"https://doi.org/10.1109/tit.2014.2357799","mag":"2062843442"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2014.2357799","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2357799","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://ir.cwi.nl/pub/22729","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012928127","display_name":"Serge Fehr","orcid":null},"institutions":[{"id":"https://openalex.org/I1341640284","display_name":"Centrum Wiskunde & Informatica","ror":"https://ror.org/00x7ekv49","country_code":"NL","type":"facility","lineage":["https://openalex.org/I1341640284","https://openalex.org/I2800991832"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Serge Fehr","raw_affiliation_strings":["Centrum Wiskunde and Informatica, Amsterdam, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Centrum Wiskunde and Informatica, Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I1341640284"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038169849","display_name":"Stefan Berens","orcid":null},"institutions":[{"id":"https://openalex.org/I121797337","display_name":"Leiden University","ror":"https://ror.org/027bh9e22","country_code":"NL","type":"education","lineage":["https://openalex.org/I121797337"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Stefan Berens","raw_affiliation_strings":["Bielefeld Graduate School of Economics and Management, Bielefeld, Germany","Mathematical Institute, Leiden University, Leiden, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Bielefeld Graduate School of Economics and Management, Bielefeld, Germany","institution_ids":[]},{"raw_affiliation_string":"Mathematical Institute, Leiden University, Leiden, The Netherlands","institution_ids":["https://openalex.org/I121797337"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5012928127"],"corresponding_institution_ids":["https://openalex.org/I1341640284"],"apc_list":null,"apc_paid":null,"fwci":6.5608,"has_fulltext":false,"cited_by_count":138,"citation_normalized_percentile":{"value":0.97233961,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"60","issue":"11","first_page":"6801","last_page":"6810"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.998199999332428,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.998199999332428,"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9746999740600586,"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/T10581","display_name":"Neural dynamics and brain function","score":0.970300018787384,"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/conditional-quantum-entropy","display_name":"Conditional quantum entropy","score":0.7861782908439636},{"id":"https://openalex.org/keywords/min-entropy","display_name":"Min entropy","score":0.7338687181472778},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.674635648727417},{"id":"https://openalex.org/keywords/r\u00e9nyi-entropy","display_name":"R\u00e9nyi entropy","score":0.6655672192573547},{"id":"https://openalex.org/keywords/joint-quantum-entropy","display_name":"Joint quantum entropy","score":0.645460844039917},{"id":"https://openalex.org/keywords/conditional-entropy","display_name":"Conditional entropy","score":0.6288843154907227},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5730655789375305},{"id":"https://openalex.org/keywords/joint-entropy","display_name":"Joint entropy","score":0.5217876434326172},{"id":"https://openalex.org/keywords/differential-entropy","display_name":"Differential entropy","score":0.4833340346813202},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.48264700174331665},{"id":"https://openalex.org/keywords/maximum-entropy-probability-distribution","display_name":"Maximum entropy probability distribution","score":0.4464586675167084},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.424893856048584},{"id":"https://openalex.org/keywords/maximum-entropy-thermodynamics","display_name":"Maximum entropy thermodynamics","score":0.42057424783706665},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3498220443725586},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.25067073106765747},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.18147149682044983},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12177738547325134},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11245819926261902},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.08221441507339478}],"concepts":[{"id":"https://openalex.org/C16609844","wikidata":"https://www.wikidata.org/wiki/Q5159273","display_name":"Conditional quantum entropy","level":5,"score":0.7861782908439636},{"id":"https://openalex.org/C196083917","wikidata":"https://www.wikidata.org/wiki/Q17103874","display_name":"Min entropy","level":5,"score":0.7338687181472778},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.674635648727417},{"id":"https://openalex.org/C142611142","wikidata":"https://www.wikidata.org/wiki/Q1433083","display_name":"R\u00e9nyi entropy","level":3,"score":0.6655672192573547},{"id":"https://openalex.org/C42047476","wikidata":"https://www.wikidata.org/wiki/Q6269544","display_name":"Joint quantum entropy","level":3,"score":0.645460844039917},{"id":"https://openalex.org/C101721835","wikidata":"https://www.wikidata.org/wiki/Q813908","display_name":"Conditional entropy","level":3,"score":0.6288843154907227},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5730655789375305},{"id":"https://openalex.org/C106752470","wikidata":"https://www.wikidata.org/wiki/Q1364826","display_name":"Joint entropy","level":3,"score":0.5217876434326172},{"id":"https://openalex.org/C124551494","wikidata":"https://www.wikidata.org/wiki/Q3055345","display_name":"Differential entropy","level":4,"score":0.4833340346813202},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.48264700174331665},{"id":"https://openalex.org/C60507348","wikidata":"https://www.wikidata.org/wiki/Q6795892","display_name":"Maximum entropy probability distribution","level":3,"score":0.4464586675167084},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.424893856048584},{"id":"https://openalex.org/C49775889","wikidata":"https://www.wikidata.org/wiki/Q6795896","display_name":"Maximum entropy thermodynamics","level":4,"score":0.42057424783706665},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3498220443725586},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.25067073106765747},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.18147149682044983},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12177738547325134},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11245819926261902},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.08221441507339478}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tit.2014.2357799","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2357799","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:cwi:oai:cwi.nl:22729","is_oa":true,"landing_page_url":"https://ir.cwi.nl/pub/22729","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Information Theory, 60(11), 6801 - 6810","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:cwi.nl:22729","is_oa":false,"landing_page_url":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6898022","pdf_url":null,"source":{"id":"https://openalex.org/S7407055335","display_name":"Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands","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":"IEEE Transactions on Information Theory vol. 60 no. 11, pp. 6801-6810","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:cwi:oai:cwi.nl:22729","is_oa":true,"landing_page_url":"https://ir.cwi.nl/pub/22729","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Information Theory, 60(11), 6801 - 6810","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1464112397","https://openalex.org/W1483547755","https://openalex.org/W1545012815","https://openalex.org/W1987805576","https://openalex.org/W1993376464","https://openalex.org/W1995875735","https://openalex.org/W2015880590","https://openalex.org/W2035245840","https://openalex.org/W2105211531","https://openalex.org/W2114921207","https://openalex.org/W2122166994","https://openalex.org/W2122882636","https://openalex.org/W2124073655","https://openalex.org/W2133738650","https://openalex.org/W2146813141","https://openalex.org/W2148587342","https://openalex.org/W2150154572","https://openalex.org/W2161579136","https://openalex.org/W2163484647","https://openalex.org/W2165203736","https://openalex.org/W2168792807","https://openalex.org/W2764347725","https://openalex.org/W3100174796","https://openalex.org/W3100438626","https://openalex.org/W3103744872","https://openalex.org/W4285719527","https://openalex.org/W6628834570","https://openalex.org/W6681877070"],"related_works":["https://openalex.org/W2062843442","https://openalex.org/W2127945237","https://openalex.org/W2952724564","https://openalex.org/W862060148","https://openalex.org/W218595706","https://openalex.org/W1574387760","https://openalex.org/W2898188192","https://openalex.org/W1992508425","https://openalex.org/W2139507220","https://openalex.org/W2045693826"],"abstract_inverted_index":{"The":[0],"R\u00e9nyi":[1,39,61,136,151,157,170],"entropy":[2,10,14,62,114,137,152,171],"of":[3,63,123,129,148,155,168],"general":[4,64],"order":[5,65],"unifies":[6],"the":[7,17,25,37,49,56,59,71,99,111,121,130,134,149,173],"well-known":[8],"Shannon":[9,26],"with":[11,163],"several":[12,41,80],"other":[13,131],"notions,":[15],"like":[16],"min-entropy":[18],"or":[19],"collision":[20],"entropy.":[21],"In":[22,51,83],"contrast":[23],"to":[24,30,116],"entropy,":[27,100],"there":[28],"seems":[29],"be":[31],"no":[32],"commonly":[33],"accepted":[34],"definition":[35,57],"for":[36,58,133],"conditional":[38,60,135,150,169],"entropy:":[40],"versions":[42],"have":[43],"been":[44],"proposed":[45,67,166],"and":[46,101,159],"used":[47],"in":[48,70,113,153,172],"literature.":[50],"this":[52,76],"paper,":[53],"we":[54,85,143,160],"reconsider":[55],"as":[66],"by":[68,120],"Arimoto":[69],"seventies.":[72],"We":[73],"show":[74,86,144,161],"that":[75,87,94,110],"particular":[77],"notion":[78,167],"satisfies":[79,89,138],"natural":[81,146],"properties.":[82,141],"particular,":[84],"it":[88],"monotonicity":[90],"under":[91],"conditioning,":[92],"meaning":[93],"conditioning":[95,117],"can":[96],"only":[97],"reduce":[98],"(a":[102],"weak":[103],"form":[104],"of)":[105],"chain":[106],"rule,":[107],"which":[108],"implies":[109],"decrease":[112],"due":[115],"is":[118],"bounded":[119],"number":[122],"bits":[124],"one":[125],"conditions":[126],"on.":[127],"None":[128],"suggestions":[132],"both":[139],"these":[140],"Finally,":[142],"a":[145,164],"interpretation":[147],"terms":[154],"(unconditional)":[156],"divergence,":[158],"consistency":[162],"recently":[165],"quantum":[174],"setting.":[175]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":14},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":17},{"year":2019,"cited_by_count":16},{"year":2018,"cited_by_count":21},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}