{"id":"https://openalex.org/W2010584937","doi":"https://doi.org/10.1109/tit.1981.1056374","title":"Maximum entropy and conditional probability","display_name":"Maximum entropy and conditional probability","publication_year":1981,"publication_date":"1981-07-01","ids":{"openalex":"https://openalex.org/W2010584937","doi":"https://doi.org/10.1109/tit.1981.1056374","mag":"2010584937"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1981.1056374","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1981.1056374","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048590409","display_name":"Jan Van Campenhout","orcid":"https://orcid.org/0000-0002-5910-1442"},"institutions":[{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"J. van Campenhout","raw_affiliation_strings":["Electronics Laboratory, State University of Ghent, Ghent, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electronics Laboratory, State University of Ghent, Ghent, Belgium","institution_ids":["https://openalex.org/I32597200"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055073921","display_name":"Thomas M. Cover","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"T. Cover","raw_affiliation_strings":["Departments of Electrical Engineering and Statistics, University of Stanford, Stanford, CA, USA","[Departments of Electrical Engineering and Statistics, University of Stanford, Stanford, CA, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departments of Electrical Engineering and Statistics, University of Stanford, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"[Departments of Electrical Engineering and Statistics, University of Stanford, Stanford, CA, USA]","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":1.2209,"has_fulltext":false,"cited_by_count":213,"citation_normalized_percentile":{"value":0.75863991,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"27","issue":"4","first_page":"483","last_page":"489"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9998000264167786,"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":0.9998000264167786,"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","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/T10622","display_name":"Quantum Mechanics and Applications","score":0.9879999756813049,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4745039641857147},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.44540444016456604},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.43612971901893616},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.38306236267089844},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.38205546140670776},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3583778440952301},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3523291051387787},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34710776805877686},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3356097936630249},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.254336416721344},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1695084571838379}],"concepts":[{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4745039641857147},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.44540444016456604},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.43612971901893616},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38306236267089844},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.38205546140670776},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3583778440952301},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3523291051387787},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34710776805877686},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3356097936630249},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.254336416721344},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1695084571838379},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"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":3,"locations":[{"id":"doi:10.1109/tit.1981.1056374","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1981.1056374","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:oai:CiteSeerX.psu:10.1.1.366.5193","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.366.5193","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-isl.stanford.edu/~cover/papers/transIT/0483camp.pdf","raw_type":"text"},{"id":"pmh:oai:archive.ugent.be:207810","is_oa":false,"landing_page_url":"http://hdl.handle.net/1854/LU-207810","pdf_url":null,"source":{"id":"https://openalex.org/S4306400478","display_name":"Ghent University Academic Bibliography (Ghent University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I32597200","host_organization_name":"Ghent University","host_organization_lineage":["https://openalex.org/I32597200"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 0018-9448","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W151155045","https://openalex.org/W1561968718","https://openalex.org/W1580334350","https://openalex.org/W1989008275","https://openalex.org/W2042587503","https://openalex.org/W2046812875","https://openalex.org/W2067596307","https://openalex.org/W2092022416","https://openalex.org/W2142901448","https://openalex.org/W2294604761","https://openalex.org/W3016217447","https://openalex.org/W4205538941","https://openalex.org/W4249186015"],"related_works":["https://openalex.org/W2951695430","https://openalex.org/W4300891849","https://openalex.org/W2318687609","https://openalex.org/W91590591","https://openalex.org/W159772521","https://openalex.org/W2950100995","https://openalex.org/W3170064006","https://openalex.org/W2281582664","https://openalex.org/W2554039769","https://openalex.org/W1997904316"],"abstract_inverted_index":{"It":[0],"is":[1,35,85],"well-known":[2],"that":[3],"maximum":[4,29,76,87],"entropy":[5,30,77,88],"distributions,":[6,31],"subject":[7],"to":[8,20,58],"appropriate":[9],"moment":[10],"constraints,":[11],"arise":[12],"in":[13],"physics":[14],"and":[15,79,96,106],"mathematics.":[16],"In":[17],"an":[18],"attempt":[19],"find":[21],"a":[22,67],"physical":[23],"reason":[24],"for":[25],"the":[26,32,41,63,71,75,80,86,102],"appearance":[27],"of":[28,66,74,94,104],"following":[33],"theorem":[34],"offered.":[36],"The":[37,92],"conditional":[38,64],"distribution":[39,65,78,84,89],"ofX_{l}given":[40],"empirical":[42],"observation(1/n)\\sum^{n}_{i}=_{l}h(X_{i})=\\alpha,":[43],"whereX_{1},X_{2},":[44],"\\cdotsare":[45],"independent":[46],"identically":[47],"distributed":[48],"random":[49,69],"variables":[50],"with":[51],"common":[52],"densitygconverges":[53],"tof_{\\lambda}(x)=e^{\\lambda^{t}h(X)}g(x)(Suitably":[54],"normalized),":[55],"where\\lambdais":[56],"chosen":[57],"satisfy\\int":[59],"f_{lambda}(x)h(x)dx=":[60],"\\alpha.":[61],"Thus":[62],"given":[68],"variableXis":[70],"(normalized)":[72],"product":[73],"initial":[81],"distribution.":[82],"This":[83],"whengis":[90],"uniform.":[91],"proof":[93],"this":[95],"related":[97],"results":[98],"relies":[99],"heavily":[100],"on":[101],"work":[103],"Zabell":[105],"Lanford.":[107]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":13},{"year":2014,"cited_by_count":12},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":7}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}