{"id":"https://openalex.org/W2052958516","doi":"https://doi.org/10.1109/tit.1980.1056144","title":"Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy","display_name":"Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy","publication_year":1980,"publication_date":"1980-01-01","ids":{"openalex":"https://openalex.org/W2052958516","doi":"https://doi.org/10.1109/tit.1980.1056144","mag":"2052958516"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1980.1056144","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1980.1056144","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://zenodo.org/record/1281582","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108223361","display_name":"John E. Shore","orcid":null},"institutions":[{"id":"https://openalex.org/I1288214837","display_name":"United States Naval Research Laboratory","ror":"https://ror.org/04d23a975","country_code":"US","type":"facility","lineage":["https://openalex.org/I1288214837","https://openalex.org/I1330347796","https://openalex.org/I175003984","https://openalex.org/I3130687028"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"J. Shore","raw_affiliation_strings":["Naval Research Laboratory, Inc., Washington D.C., DC, USA","[Naval Research Laboratory, Inc., Washington D.C., DC, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Naval Research Laboratory, Inc., Washington D.C., DC, USA","institution_ids":["https://openalex.org/I1288214837"]},{"raw_affiliation_string":"[Naval Research Laboratory, Inc., Washington D.C., DC, USA]","institution_ids":["https://openalex.org/I1288214837"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101427209","display_name":"Ryan F. Johnson","orcid":"https://orcid.org/0000-0003-1246-8076"},"institutions":[{"id":"https://openalex.org/I1288214837","display_name":"United States Naval Research Laboratory","ror":"https://ror.org/04d23a975","country_code":"US","type":"facility","lineage":["https://openalex.org/I1288214837","https://openalex.org/I1330347796","https://openalex.org/I175003984","https://openalex.org/I3130687028"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"R. Johnson","raw_affiliation_strings":["Naval Research Laboratory, Inc., Washington D.C., DC, USA","[Naval Research Laboratory, Inc., Washington D.C., DC, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Naval Research Laboratory, Inc., Washington D.C., DC, USA","institution_ids":["https://openalex.org/I1288214837"]},{"raw_affiliation_string":"[Naval Research Laboratory, Inc., Washington D.C., DC, USA]","institution_ids":["https://openalex.org/I1288214837"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5108223361"],"corresponding_institution_ids":["https://openalex.org/I1288214837"],"apc_list":null,"apc_paid":null,"fwci":16.7699,"has_fulltext":false,"cited_by_count":1795,"citation_normalized_percentile":{"value":0.99771885,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"26","issue":"1","first_page":"26","last_page":"37"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9991999864578247,"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":0.9991999864578247,"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/T10778","display_name":"Philosophy and History of Science","score":0.9779999852180481,"subfield":{"id":"https://openalex.org/subfields/1207","display_name":"History and Philosophy of Science"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9664999842643738,"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/mathematics","display_name":"Mathematics","score":0.7320489287376404},{"id":"https://openalex.org/keywords/maximum-entropy-thermodynamics","display_name":"Maximum entropy thermodynamics","score":0.7238010168075562},{"id":"https://openalex.org/keywords/maximum-entropy-probability-distribution","display_name":"Maximum entropy probability distribution","score":0.7004361748695374},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.6661850810050964},{"id":"https://openalex.org/keywords/joint-entropy","display_name":"Joint entropy","score":0.6226327419281006},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5674935579299927},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.5625836849212646},{"id":"https://openalex.org/keywords/minimum-description-length","display_name":"Minimum description length","score":0.5057864189147949},{"id":"https://openalex.org/keywords/min-entropy","display_name":"Min entropy","score":0.47371405363082886},{"id":"https://openalex.org/keywords/joint-quantum-entropy","display_name":"Joint quantum entropy","score":0.4637957215309143},{"id":"https://openalex.org/keywords/differential-entropy","display_name":"Differential entropy","score":0.4630807340145111},{"id":"https://openalex.org/keywords/maximum-entropy-spectral-estimation","display_name":"Maximum entropy spectral estimation","score":0.4587135910987854},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.4188220500946045},{"id":"https://openalex.org/keywords/entropy-rate","display_name":"Entropy rate","score":0.4107881486415863},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3585592210292816},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20483124256134033},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.14054161310195923}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7320489287376404},{"id":"https://openalex.org/C49775889","wikidata":"https://www.wikidata.org/wiki/Q6795896","display_name":"Maximum entropy thermodynamics","level":4,"score":0.7238010168075562},{"id":"https://openalex.org/C60507348","wikidata":"https://www.wikidata.org/wiki/Q6795892","display_name":"Maximum entropy probability distribution","level":3,"score":0.7004361748695374},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.6661850810050964},{"id":"https://openalex.org/C106752470","wikidata":"https://www.wikidata.org/wiki/Q1364826","display_name":"Joint entropy","level":3,"score":0.6226327419281006},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5674935579299927},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5625836849212646},{"id":"https://openalex.org/C87465248","wikidata":"https://www.wikidata.org/wiki/Q1417790","display_name":"Minimum description length","level":2,"score":0.5057864189147949},{"id":"https://openalex.org/C196083917","wikidata":"https://www.wikidata.org/wiki/Q17103874","display_name":"Min entropy","level":5,"score":0.47371405363082886},{"id":"https://openalex.org/C42047476","wikidata":"https://www.wikidata.org/wiki/Q6269544","display_name":"Joint quantum entropy","level":3,"score":0.4637957215309143},{"id":"https://openalex.org/C124551494","wikidata":"https://www.wikidata.org/wiki/Q3055345","display_name":"Differential entropy","level":4,"score":0.4630807340145111},{"id":"https://openalex.org/C89735579","wikidata":"https://www.wikidata.org/wiki/Q6795894","display_name":"Maximum entropy spectral estimation","level":3,"score":0.4587135910987854},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.4188220500946045},{"id":"https://openalex.org/C125252325","wikidata":"https://www.wikidata.org/wiki/Q1345213","display_name":"Entropy rate","level":4,"score":0.4107881486415863},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3585592210292816},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20483124256134033},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.14054161310195923},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tit.1980.1056144","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1980.1056144","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:ADA063120","is_oa":false,"landing_page_url":"http://oai.dtic.mil/oai/oai?&amp;verb=getRecord&amp;metadataPrefix=html&amp;identifier=ADA063120","pdf_url":null,"source":{"id":"https://openalex.org/S4406923043","display_name":"Defense Technical Information Center (DTIC)","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":"DTIC AND NTIS","raw_type":"Text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.646.2507","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.646.2507","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://bayes.wustl.edu/Manual/AxiomaticDerivation.pdf","raw_type":"text"},{"id":"pmh:oai:zenodo.org:1281582","is_oa":true,"landing_page_url":"https://zenodo.org/record/1281582","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:zenodo.org:1281582","is_oa":true,"landing_page_url":"https://zenodo.org/record/1281582","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","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":65,"referenced_works":["https://openalex.org/W365884688","https://openalex.org/W562957111","https://openalex.org/W630957616","https://openalex.org/W642705176","https://openalex.org/W1531408481","https://openalex.org/W1593125407","https://openalex.org/W1654590594","https://openalex.org/W1968076658","https://openalex.org/W1980304447","https://openalex.org/W1980763425","https://openalex.org/W1992578604","https://openalex.org/W1993690418","https://openalex.org/W1995875735","https://openalex.org/W1997187158","https://openalex.org/W1998234377","https://openalex.org/W2005391990","https://openalex.org/W2006681603","https://openalex.org/W2010584937","https://openalex.org/W2014960773","https://openalex.org/W2025130480","https://openalex.org/W2026216742","https://openalex.org/W2032558547","https://openalex.org/W2034327144","https://openalex.org/W2038066559","https://openalex.org/W2051445572","https://openalex.org/W2052958516","https://openalex.org/W2055137423","https://openalex.org/W2060692908","https://openalex.org/W2072973836","https://openalex.org/W2074627567","https://openalex.org/W2085294315","https://openalex.org/W2087171258","https://openalex.org/W2089194925","https://openalex.org/W2089611415","https://openalex.org/W2090348360","https://openalex.org/W2093965945","https://openalex.org/W2095512634","https://openalex.org/W2123838014","https://openalex.org/W2132930716","https://openalex.org/W2134316164","https://openalex.org/W2139494290","https://openalex.org/W2151252878","https://openalex.org/W2154945989","https://openalex.org/W2159961921","https://openalex.org/W2160709761","https://openalex.org/W2183406252","https://openalex.org/W2187039764","https://openalex.org/W2196893271","https://openalex.org/W2294604761","https://openalex.org/W2317912355","https://openalex.org/W2321706177","https://openalex.org/W2796444471","https://openalex.org/W2798646345","https://openalex.org/W2801129195","https://openalex.org/W2808650095","https://openalex.org/W2953016690","https://openalex.org/W3015462599","https://openalex.org/W3093664000","https://openalex.org/W4241085363","https://openalex.org/W4246675730","https://openalex.org/W4249186015","https://openalex.org/W4252028749","https://openalex.org/W4319590843","https://openalex.org/W6784656030","https://openalex.org/W6948883466"],"related_works":["https://openalex.org/W2955910739","https://openalex.org/W862060148","https://openalex.org/W2898188192","https://openalex.org/W2139507220","https://openalex.org/W4226181437","https://openalex.org/W4313555435","https://openalex.org/W2744108151","https://openalex.org/W4385760565","https://openalex.org/W2034921015","https://openalex.org/W2884476384"],"abstract_inverted_index":{"Jaynes's":[0],"principle":[1,7,115,203],"of":[2,8,32,45,59,72,98,116,150,197,204],"maximum":[3,117],"entropy":[4,46,118,129,138],"and":[5,40,47,103,137,190,215],"Kullbacks":[6],"minimum":[9,205],"cross-entropy":[10,48],"(minimum":[11],"directed":[12],"divergence)":[13],"are":[14,69,94,208],"shown":[15],"to":[16,64,107,132],"be":[17,165,179],"uniquely":[18],"correct":[19,120],"methods":[20,58],"for":[21,201,211,216],"inductive":[22,60],"inference":[23,61],"when":[24,67],"new":[25],"information":[26,50,76,101,108,146],"is":[27,87,111,119,156,186],"given":[28,145],"in":[29,81,96,121,147],"the":[30,43,74,114,122,148,161,172,202],"form":[31,149],"expected":[33,153],"values.":[34],"Previous":[35],"justifications":[36],"use":[37],"intuitive":[38],"arguments":[39],"rely":[41],"on":[42,152],"properties":[44],"as":[49,89,191],"measures.":[51,109],"The":[52],"approach":[53],"here":[54],"assumes":[55],"that":[56,113,135,163,170],"reasonable":[57],"should":[62],"lead":[63,131],"consistent":[65],"results":[66],"there":[68,155],"different":[70,82],"ways":[71],"taking":[73],"same":[75],"into":[77],"account":[78],"(for":[79],"example,":[80],"coordinate":[83],"system).":[84],"This":[85,184],"requirement":[86],"formalized":[88],"four":[90],"consistency":[91,173],"axioms.":[92],"These":[93],"stated":[95],"terms":[97],"an":[99,198],"abstract":[100],"operator":[102],"make":[104],"no":[105],"reference":[106],"It":[110],"proved":[112],"following":[123],"sense:":[124],"maximizing":[125,182],"any":[126],"function":[127,136],"but":[128],"will":[130],"inconsistency":[133],"unless":[134],"have":[139],"identical":[140],"maxima.":[141],"In":[142],"other":[143],"words":[144],"constraints":[151,162],"values,":[154],"only":[157],"one":[158],"(distribution":[159],"satisfying":[160],"can":[164,178],"chosen":[166],"by":[167,181],"a":[168,192],"procedure":[169],"satisfies":[171],"axioms;":[174],"this":[175],"unique":[176],"distribution":[177],"obtained":[180,209],"entropy.":[183],"result":[185,200],"established":[187],"both":[188,210],"directly":[189],"special":[193],"case":[194],"(uniform":[195],"priors)":[196],"analogous":[199],"cross-entropy.":[206],"Results":[207],"continuous":[212],"probability":[213],"densities":[214],"discrete":[217],"distributions.":[218]},"counts_by_year":[{"year":2026,"cited_by_count":19},{"year":2025,"cited_by_count":45},{"year":2024,"cited_by_count":46},{"year":2023,"cited_by_count":46},{"year":2022,"cited_by_count":66},{"year":2021,"cited_by_count":82},{"year":2020,"cited_by_count":70},{"year":2019,"cited_by_count":83},{"year":2018,"cited_by_count":69},{"year":2017,"cited_by_count":62},{"year":2016,"cited_by_count":35},{"year":2015,"cited_by_count":53},{"year":2014,"cited_by_count":47},{"year":2013,"cited_by_count":58},{"year":2012,"cited_by_count":39}],"updated_date":"2026-04-25T08:17:42.794288","created_date":"2025-10-10T00:00:00"}
