{"id":"https://openalex.org/W7127174704","doi":"https://doi.org/10.3390/computation14020042","title":"Information Inequalities for Five Random Variables","display_name":"Information Inequalities for Five Random Variables","publication_year":2026,"publication_date":"2026-02-02","ids":{"openalex":"https://openalex.org/W7127174704","doi":"https://doi.org/10.3390/computation14020042"},"language":"en","primary_location":{"id":"doi:10.3390/computation14020042","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation14020042","pdf_url":null,"source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"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":"Computation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/computation14020042","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090277124","display_name":"L\u00e1szl\u00f3 Csirmaz","orcid":"https://orcid.org/0000-0001-7530-8307"},"institutions":[{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]},{"id":"https://openalex.org/I4210119419","display_name":"Czech Academy of Sciences, Institute of Information Theory and Automation","ror":"https://ror.org/03h1hsz49","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210119419"]}],"countries":["CZ","HU"],"is_corresponding":false,"raw_author_name":"Laszlo Csirmaz","raw_affiliation_strings":["Alfr\u00e9d R\u00e9nyi Institute of Mathematics, 1053 Budapest, Hungary","Institute of Information Theory and Automation, CZ-182 00 Prague, Czech Republic"],"raw_orcid":"https://orcid.org/0000-0001-7530-8307","affiliations":[{"raw_affiliation_string":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics, 1053 Budapest, Hungary","institution_ids":["https://openalex.org/I127817813"]},{"raw_affiliation_string":"Institute of Information Theory and Automation, CZ-182 00 Prague, Czech Republic","institution_ids":["https://openalex.org/I4210119419"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008129984","display_name":"Elod P. Csirmaz","orcid":"https://orcid.org/0000-0003-2449-7923"},"institutions":[{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"Elod P. Csirmaz","raw_affiliation_strings":["Alfr\u00e9d R\u00e9nyi Institute of Mathematics, 1053 Budapest, Hungary"],"raw_orcid":"https://orcid.org/0000-0003-2449-7923","affiliations":[{"raw_affiliation_string":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics, 1053 Budapest, Hungary","institution_ids":["https://openalex.org/I127817813"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13071139,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"2","first_page":"42","last_page":"42"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.09560000151395798,"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/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.09560000151395798,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.0794999971985817,"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/T11130","display_name":"Coding theory and cryptography","score":0.07720000296831131,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/entropy-power-inequality","display_name":"Entropy power inequality","score":0.7067999839782715},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.6061999797821045},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.5717999935150146},{"id":"https://openalex.org/keywords/r\u00e9nyi-entropy","display_name":"R\u00e9nyi entropy","score":0.51419997215271},{"id":"https://openalex.org/keywords/information-theory","display_name":"Information theory","score":0.41440001130104065},{"id":"https://openalex.org/keywords/maximum-entropy-probability-distribution","display_name":"Maximum entropy probability distribution","score":0.39340001344680786},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.3785000145435333},{"id":"https://openalex.org/keywords/conditional-entropy","display_name":"Conditional entropy","score":0.35659998655319214}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8367000222206116},{"id":"https://openalex.org/C320580","wikidata":"https://www.wikidata.org/wiki/Q5380810","display_name":"Entropy power inequality","level":5,"score":0.7067999839782715},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.6061999797821045},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.5717999935150146},{"id":"https://openalex.org/C142611142","wikidata":"https://www.wikidata.org/wiki/Q1433083","display_name":"R\u00e9nyi entropy","level":3,"score":0.51419997215271},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41780000925064087},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.41440001130104065},{"id":"https://openalex.org/C60507348","wikidata":"https://www.wikidata.org/wiki/Q6795892","display_name":"Maximum entropy probability distribution","level":3,"score":0.39340001344680786},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.3785000145435333},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.359499990940094},{"id":"https://openalex.org/C101721835","wikidata":"https://www.wikidata.org/wiki/Q813908","display_name":"Conditional entropy","level":3,"score":0.35659998655319214},{"id":"https://openalex.org/C196083917","wikidata":"https://www.wikidata.org/wiki/Q17103874","display_name":"Min entropy","level":5,"score":0.35260000824928284},{"id":"https://openalex.org/C42047476","wikidata":"https://www.wikidata.org/wiki/Q6269544","display_name":"Joint quantum entropy","level":3,"score":0.3515999913215637},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.34549999237060547},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.3452000021934509},{"id":"https://openalex.org/C106752470","wikidata":"https://www.wikidata.org/wiki/Q1364826","display_name":"Joint entropy","level":3,"score":0.34290000796318054},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3188000023365021},{"id":"https://openalex.org/C44415725","wikidata":"https://www.wikidata.org/wiki/Q4913893","display_name":"Binary entropy function","level":3,"score":0.30090001225471497},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.28049999475479126},{"id":"https://openalex.org/C24495805","wikidata":"https://www.wikidata.org/wiki/Q7269091","display_name":"Quantum relative entropy","level":5,"score":0.274399995803833}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/computation14020042","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation14020042","pdf_url":null,"source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"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":"Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2512.23316","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.23316","pdf_url":"https://arxiv.org/pdf/2512.23316","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,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:ee8ccff520e348efb2cb6619f4f9cb1a","is_oa":false,"landing_page_url":"https://doaj.org/article/ee8ccff520e348efb2cb6619f4f9cb1a","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":"Computation, Vol 14, Iss 2, p 42 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/computation14020042","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation14020042","pdf_url":null,"source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"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":"Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.5594756603240967,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0,144],"entropic":[1,32],"region":[2,33],"is":[3,34,150],"formed":[4],"by":[5,81,95],"the":[6,9,28,31,42,54,65,83,96,102,154],"collection":[7],"of":[8,12,15,30,41,62,64,109,123,147],"Shannon":[10],"entropies":[11],"all":[13,90,141],"subvectors":[14],"finitely":[16],"many":[17],"jointly":[18],"distributed":[19],"discrete":[20],"random":[21,66],"variables.":[22],"For":[23],"four":[24],"or":[25],"more":[26],"variables,":[27],"structure":[29],"mostly":[35],"unknown.":[36],"We":[37,119],"utilize":[38],"a":[39],"variant":[40],"Maximum":[43],"Entropy":[44],"Method":[45],"to":[46,88,115,139,152],"obtain":[47],"five-variable":[48,55,91],"non-Shannon":[49,92],"entropy":[50,56,117,148],"inequalities,":[51],"which":[52],"delimit":[53],"region.":[57],"This":[58],"method":[59,156],"adds":[60],"copies":[61],"some":[63],"variables":[67],"in":[68,73],"generations.":[69,99],"A":[70],"significant":[71],"reduction":[72],"computational":[74],"complexity,":[75],"achieved":[76],"through":[77],"theoretical":[78],"considerations":[79],"and":[80,112,131],"harnessing":[82],"inherent":[84],"symmetries,":[85],"allowed":[86],"us":[87],"calculate":[89],"inequalities":[93,111,149],"provided":[94],"first":[97],"nine":[98],"Based":[100],"on":[101,133],"results,":[103],"we":[104,135],"define":[105],"two":[106],"infinite":[107],"collections":[108],"such":[110],"prove":[113],"them":[114],"be":[116],"inequalities.":[118,143],"investigate":[120],"downward-closed":[121],"subsets":[122],"non-negative":[124],"lattice":[125],"points":[126],"that":[127],"parameterize":[128],"these":[129],"collections,":[130],"based":[132],"this,":[134],"develop":[136],"an":[137],"algorithm":[138],"enumerate":[140],"extremal":[142],"discovered":[145],"set":[146],"conjectured":[151],"characterize":[153],"applied":[155],"completely.":[157]},"counts_by_year":[],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2026-02-03T00:00:00"}
