{"id":"https://openalex.org/W1980182342","doi":"https://doi.org/10.1016/s0019-9958(59)90082-8","title":"Entropy and the uncertainty principle","display_name":"Entropy and the uncertainty principle","publication_year":1959,"publication_date":"1959-04-01","ids":{"openalex":"https://openalex.org/W1980182342","doi":"https://doi.org/10.1016/s0019-9958(59)90082-8","mag":"1980182342"},"language":"en","primary_location":{"id":"doi:10.1016/s0019-9958(59)90082-8","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0019-9958(59)90082-8","pdf_url":null,"source":{"id":"https://openalex.org/S4210192454","display_name":"Information and Control","issn_l":"0019-9958","issn":["0019-9958","1878-2981"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319955","host_organization_name":"Academic Press","host_organization_lineage":["https://openalex.org/P4310319955","https://openalex.org/P4310320990"],"host_organization_lineage_names":["Academic Press","Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Information and Control","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/A5028415858","display_name":"Roy B. Leipnik","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Roy Leipnik","raw_affiliation_strings":["Test Department, US NOTS, China Lake, California, USA"],"affiliations":[{"raw_affiliation_string":"Test Department, US NOTS, China Lake, California, USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5028415858"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8759,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.684514,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"2","issue":"1","first_page":"64","last_page":"79"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9994000196456909,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.9994000196456909,"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9847000241279602,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9747999906539917,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/uncertainty-principle","display_name":"Uncertainty principle","score":0.8094043135643005},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.6877809166908264},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6346078515052795},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.6271541118621826},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.546749472618103},{"id":"https://openalex.org/keywords/entropic-uncertainty","display_name":"Entropic uncertainty","score":0.5219173431396484},{"id":"https://openalex.org/keywords/observable","display_name":"Observable","score":0.5054354667663574},{"id":"https://openalex.org/keywords/joint-entropy","display_name":"Joint entropy","score":0.49213212728500366},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.42343869805336},{"id":"https://openalex.org/keywords/maximum-entropy-probability-distribution","display_name":"Maximum entropy probability distribution","score":0.4220249056816101},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.40540069341659546},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33857861161231995},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3193240761756897},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.22649547457695007},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.16378554701805115},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.0695180892944336}],"concepts":[{"id":"https://openalex.org/C181543814","wikidata":"https://www.wikidata.org/wiki/Q44746","display_name":"Uncertainty principle","level":3,"score":0.8094043135643005},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.6877809166908264},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6346078515052795},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.6271541118621826},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.546749472618103},{"id":"https://openalex.org/C37731324","wikidata":"https://www.wikidata.org/wiki/Q5380783","display_name":"Entropic uncertainty","level":4,"score":0.5219173431396484},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.5054354667663574},{"id":"https://openalex.org/C106752470","wikidata":"https://www.wikidata.org/wiki/Q1364826","display_name":"Joint entropy","level":3,"score":0.49213212728500366},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.42343869805336},{"id":"https://openalex.org/C60507348","wikidata":"https://www.wikidata.org/wiki/Q6795892","display_name":"Maximum entropy probability distribution","level":3,"score":0.4220249056816101},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.40540069341659546},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33857861161231995},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3193240761756897},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.22649547457695007},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.16378554701805115},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0695180892944336}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0019-9958(59)90082-8","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0019-9958(59)90082-8","pdf_url":null,"source":{"id":"https://openalex.org/S4210192454","display_name":"Information and Control","issn_l":"0019-9958","issn":["0019-9958","1878-2981"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319955","host_organization_name":"Academic Press","host_organization_lineage":["https://openalex.org/P4310319955","https://openalex.org/P4310320990"],"host_organization_lineage_names":["Academic Press","Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Information and Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1558198063","https://openalex.org/W1633992798","https://openalex.org/W1992649154","https://openalex.org/W1995875735","https://openalex.org/W2022708042","https://openalex.org/W2031451638","https://openalex.org/W2042601507","https://openalex.org/W2043371182","https://openalex.org/W2090099030","https://openalex.org/W2094672213","https://openalex.org/W2170649178","https://openalex.org/W2320045903","https://openalex.org/W2596773272","https://openalex.org/W3165898261","https://openalex.org/W6633402864","https://openalex.org/W6655773005","https://openalex.org/W6685277109"],"related_works":["https://openalex.org/W3104780148","https://openalex.org/W2057233237","https://openalex.org/W1990645539","https://openalex.org/W3206579266","https://openalex.org/W2955910739","https://openalex.org/W2176894780","https://openalex.org/W2088696280","https://openalex.org/W3116753919","https://openalex.org/W1980182342","https://openalex.org/W3017803990"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}