{"id":"https://openalex.org/W1968021238","doi":"https://doi.org/10.1109/tit.2014.2338852","title":"Beyond the Entropy Power Inequality, via Rearrangements","display_name":"Beyond the Entropy Power Inequality, via Rearrangements","publication_year":2014,"publication_date":"2014-07-14","ids":{"openalex":"https://openalex.org/W1968021238","doi":"https://doi.org/10.1109/tit.2014.2338852","mag":"1968021238"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2014.2338852","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2338852","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1307.6018","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034420463","display_name":"Liyao Wang","orcid":"https://orcid.org/0000-0002-8931-7367"},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Liyao Wang","raw_affiliation_strings":["Department of Physics, Yale University, New Haven, CT, USA","[Dept. of Phys., Yale Univ., New Haven, CT, USA]"],"affiliations":[{"raw_affiliation_string":"Department of Physics, Yale University, New Haven, CT, USA","institution_ids":["https://openalex.org/I32971472"]},{"raw_affiliation_string":"[Dept. of Phys., Yale Univ., New Haven, CT, USA]","institution_ids":["https://openalex.org/I32971472"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089127356","display_name":"Mokshay Madiman","orcid":"https://orcid.org/0000-0002-2992-1829"},"institutions":[{"id":"https://openalex.org/I86501945","display_name":"University of Delaware","ror":"https://ror.org/01sbq1a82","country_code":"US","type":"education","lineage":["https://openalex.org/I86501945"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mokshay Madiman","raw_affiliation_strings":["Department of Mathematical Sciences, University of Delaware, Newark, DE, USA","Dept. of Math. Sci., Univ. of Delaware, Newark, DE, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of Delaware, Newark, DE, USA","institution_ids":["https://openalex.org/I86501945"]},{"raw_affiliation_string":"Dept. of Math. Sci., Univ. of Delaware, Newark, DE, USA","institution_ids":["https://openalex.org/I86501945"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5034420463"],"corresponding_institution_ids":["https://openalex.org/I32971472"],"apc_list":null,"apc_paid":null,"fwci":5.7445,"has_fulltext":false,"cited_by_count":76,"citation_normalized_percentile":{"value":0.96443044,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"60","issue":"9","first_page":"5116","last_page":"5137"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","score":0.9916999936103821,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","score":0.9916999936103821,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9896000027656555,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9810000061988831,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/entropy-power-inequality","display_name":"Entropy power inequality","score":0.8998939990997314},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7974218726158142},{"id":"https://openalex.org/keywords/differential-entropy","display_name":"Differential entropy","score":0.7511568069458008},{"id":"https://openalex.org/keywords/symmetrization","display_name":"Symmetrization","score":0.6876474022865295},{"id":"https://openalex.org/keywords/maximum-entropy-probability-distribution","display_name":"Maximum entropy probability distribution","score":0.6444814205169678},{"id":"https://openalex.org/keywords/joint-quantum-entropy","display_name":"Joint quantum entropy","score":0.6140884757041931},{"id":"https://openalex.org/keywords/r\u00e9nyi-entropy","display_name":"R\u00e9nyi entropy","score":0.5876641869544983},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5699049830436707},{"id":"https://openalex.org/keywords/quantum-relative-entropy","display_name":"Quantum relative entropy","score":0.5667729377746582},{"id":"https://openalex.org/keywords/min-entropy","display_name":"Min entropy","score":0.5416619777679443},{"id":"https://openalex.org/keywords/maximum-entropy-thermodynamics","display_name":"Maximum entropy thermodynamics","score":0.5029627680778503},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4686058759689331},{"id":"https://openalex.org/keywords/entropy-rate","display_name":"Entropy rate","score":0.45517992973327637},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.3731788992881775},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.36222994327545166},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3230048418045044},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22654607892036438},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.15735524892807007},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13723883032798767},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.07871446013450623},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07716789841651917}],"concepts":[{"id":"https://openalex.org/C320580","wikidata":"https://www.wikidata.org/wiki/Q5380810","display_name":"Entropy power inequality","level":5,"score":0.8998939990997314},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7974218726158142},{"id":"https://openalex.org/C124551494","wikidata":"https://www.wikidata.org/wiki/Q3055345","display_name":"Differential entropy","level":4,"score":0.7511568069458008},{"id":"https://openalex.org/C64999384","wikidata":"https://www.wikidata.org/wiki/Q3507967","display_name":"Symmetrization","level":2,"score":0.6876474022865295},{"id":"https://openalex.org/C60507348","wikidata":"https://www.wikidata.org/wiki/Q6795892","display_name":"Maximum entropy probability distribution","level":3,"score":0.6444814205169678},{"id":"https://openalex.org/C42047476","wikidata":"https://www.wikidata.org/wiki/Q6269544","display_name":"Joint quantum entropy","level":3,"score":0.6140884757041931},{"id":"https://openalex.org/C142611142","wikidata":"https://www.wikidata.org/wiki/Q1433083","display_name":"R\u00e9nyi entropy","level":3,"score":0.5876641869544983},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5699049830436707},{"id":"https://openalex.org/C24495805","wikidata":"https://www.wikidata.org/wiki/Q7269091","display_name":"Quantum relative entropy","level":5,"score":0.5667729377746582},{"id":"https://openalex.org/C196083917","wikidata":"https://www.wikidata.org/wiki/Q17103874","display_name":"Min entropy","level":5,"score":0.5416619777679443},{"id":"https://openalex.org/C49775889","wikidata":"https://www.wikidata.org/wiki/Q6795896","display_name":"Maximum entropy thermodynamics","level":4,"score":0.5029627680778503},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4686058759689331},{"id":"https://openalex.org/C125252325","wikidata":"https://www.wikidata.org/wiki/Q1345213","display_name":"Entropy rate","level":4,"score":0.45517992973327637},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.3731788992881775},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.36222994327545166},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3230048418045044},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22654607892036438},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.15735524892807007},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13723883032798767},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.07871446013450623},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07716789841651917},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"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/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2014.2338852","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2338852","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:arXiv.org:1307.6018","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1307.6018","pdf_url":"https://arxiv.org/pdf/1307.6018","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1307.6018","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1307.6018","pdf_url":"https://arxiv.org/pdf/1307.6018","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.6000000238418579}],"awards":[{"id":"https://openalex.org/G1046991289","display_name":null,"funder_award_id":"CCF-1346564","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8357027711","display_name":null,"funder_award_id":"DMS-1409504","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320308380","display_name":"Yale University","ror":"https://ror.org/03v76x132"},{"id":"https://openalex.org/F4320310071","display_name":"Indian Institute of Science","ror":"https://ror.org/04dese585"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":60,"referenced_works":["https://openalex.org/W157108002","https://openalex.org/W159610323","https://openalex.org/W1551558821","https://openalex.org/W1594563152","https://openalex.org/W1803411289","https://openalex.org/W1829604380","https://openalex.org/W1918806379","https://openalex.org/W1987278905","https://openalex.org/W1993000235","https://openalex.org/W1995522593","https://openalex.org/W1995875735","https://openalex.org/W2002867407","https://openalex.org/W2010141925","https://openalex.org/W2012726532","https://openalex.org/W2017518369","https://openalex.org/W2019935882","https://openalex.org/W2026653933","https://openalex.org/W2033823299","https://openalex.org/W2034579567","https://openalex.org/W2037356780","https://openalex.org/W2039496964","https://openalex.org/W2041295460","https://openalex.org/W2043371182","https://openalex.org/W2046539811","https://openalex.org/W2049932919","https://openalex.org/W2056129277","https://openalex.org/W2063555056","https://openalex.org/W2066614043","https://openalex.org/W2088575247","https://openalex.org/W2094654291","https://openalex.org/W2096042755","https://openalex.org/W2102646476","https://openalex.org/W2103513336","https://openalex.org/W2121952483","https://openalex.org/W2123901758","https://openalex.org/W2133318567","https://openalex.org/W2162337698","https://openalex.org/W2169690298","https://openalex.org/W2258578877","https://openalex.org/W2275286668","https://openalex.org/W2295183364","https://openalex.org/W2315996107","https://openalex.org/W2327680971","https://openalex.org/W2478708596","https://openalex.org/W2964286746","https://openalex.org/W2993383518","https://openalex.org/W3021947329","https://openalex.org/W3098235725","https://openalex.org/W3144969279","https://openalex.org/W4240422944","https://openalex.org/W4240643369","https://openalex.org/W4244292443","https://openalex.org/W4293875981","https://openalex.org/W4300859130","https://openalex.org/W4301258660","https://openalex.org/W4301650748","https://openalex.org/W6647204613","https://openalex.org/W6692582951","https://openalex.org/W6697200512","https://openalex.org/W6792728667"],"related_works":["https://openalex.org/W2898188192","https://openalex.org/W3024670026","https://openalex.org/W862060148","https://openalex.org/W3185559999","https://openalex.org/W2127945237","https://openalex.org/W2300741437","https://openalex.org/W2037356780","https://openalex.org/W3114186922","https://openalex.org/W2330170324","https://openalex.org/W2952724564"],"abstract_inverted_index":{"A":[0],"lower":[1,29],"bound":[2,30],"on":[3],"the":[4,22,37,50],"R\u00e9nyi":[5],"differential":[6],"entropy":[7,38,52,57],"of":[8,11,19,25,49,61],"a":[9,46],"sum":[10],"independent":[12],"random":[13],"vectors":[14],"is":[15,31],"demonstrated":[16],"in":[17],"terms":[18],"rearrangements.":[20],"For":[21],"special":[23],"case":[24],"Boltzmann-Shannon":[26],"entropy,":[27],"this":[28],"better":[32],"than":[33],"that":[34],"given":[35],"by":[36],"power":[39,53],"inequality.":[40],"Several":[41],"applications":[42],"are":[43],"discussed,":[44],"including":[45],"new":[47],"proof":[48],"classical":[51],"inequality":[54,58],"and":[55],"an":[56],"involving":[59],"symmetrization":[60],"L\u00e9vy":[62],"processes.":[63]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
