{"id":"https://openalex.org/W7214671192","doi":"https://doi.org/10.48550/arxiv.2609.30284","title":"Von Neumann's Two Quantum Entropies","display_name":"Von Neumann's Two Quantum Entropies","publication_year":2026,"publication_date":"2026-09-03","ids":{"openalex":"https://openalex.org/W7214671192","doi":"https://doi.org/10.48550/arxiv.2609.30284"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.30284","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.30284","pdf_url":"https://arxiv.org/pdf/2609.30284","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,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.30284","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153216899","display_name":"Biao Wu","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Wu, Biao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5153216899"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.475600004196167,"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":0.475600004196167,"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":0.2759000062942505,"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":0.20020000636577606,"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/von-neumann-entropy","display_name":"von Neumann entropy","score":0.9879999756813049},{"id":"https://openalex.org/keywords/quantum-entropy","display_name":"quantum entropy","score":0.7409999966621399},{"id":"https://openalex.org/keywords/thermodynamic-entropy","display_name":"thermodynamic entropy","score":0.8539999723434448},{"id":"https://openalex.org/keywords/quantum-states","display_name":"quantum states","score":0.652999997138977},{"id":"https://openalex.org/keywords/entanglement-measures","display_name":"entanglement measures","score":0.8339999914169312},{"id":"https://openalex.org/keywords/history-of-quantum-mechanics","display_name":"history of quantum mechanics","score":0.7839999794960022},{"id":"https://openalex.org/keywords/pure-states","display_name":"pure states","score":0.6439999938011169}],"concepts":[{"id":"https://openalex.org/C101973423","wikidata":"https://www.wikidata.org/wiki/Q6961323","display_name":"Von Neumann entropy","level":4,"score":0.843999981880188},{"id":"https://openalex.org/C42047476","wikidata":"https://www.wikidata.org/wiki/Q6269544","display_name":"Joint quantum entropy","level":3,"score":0.7124999761581421},{"id":"https://openalex.org/C24495805","wikidata":"https://www.wikidata.org/wiki/Q7269091","display_name":"Quantum relative entropy","level":5,"score":0.6444000005722046},{"id":"https://openalex.org/C5084201","wikidata":"https://www.wikidata.org/wiki/Q17090689","display_name":"Generalized relative entropy","level":5,"score":0.5893999934196472},{"id":"https://openalex.org/C64775481","wikidata":"https://www.wikidata.org/wiki/Q3798613","display_name":"Quantum mutual information","level":5,"score":0.5834000110626221},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5759999752044678},{"id":"https://openalex.org/C16609844","wikidata":"https://www.wikidata.org/wiki/Q5159273","display_name":"Conditional quantum entropy","level":5,"score":0.54339998960495},{"id":"https://openalex.org/C139356082","wikidata":"https://www.wikidata.org/wiki/Q7269038","display_name":"Quantum discord","level":4,"score":0.5218999981880188},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4862000048160553},{"id":"https://openalex.org/C148563202","wikidata":"https://www.wikidata.org/wiki/Q5380803","display_name":"Entropy in thermodynamics and information theory","level":5,"score":0.46299999952316284},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4611000120639801},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.414900004863739},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.37549999356269836},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.37040001153945923},{"id":"https://openalex.org/C80469333","wikidata":"https://www.wikidata.org/wiki/Q189088","display_name":"Von Neumann architecture","level":2,"score":0.365200012922287},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.34950000047683716},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3310999870300293},{"id":"https://openalex.org/C33932047","wikidata":"https://www.wikidata.org/wiki/Q375553","display_name":"Boltzmann's entropy formula","level":3,"score":0.32820001244544983},{"id":"https://openalex.org/C142611142","wikidata":"https://www.wikidata.org/wiki/Q1433083","display_name":"R\u00e9nyi entropy","level":3,"score":0.2978000044822693},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.2858000099658966},{"id":"https://openalex.org/C14828074","wikidata":"https://www.wikidata.org/wiki/Q186559","display_name":"Arrow of time","level":3,"score":0.2669000029563904},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.2646999955177307}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.30284","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.30284","pdf_url":"https://arxiv.org/pdf/2609.30284","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,"listed_in":[],"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"},{"id":"doi:10.48550/arxiv.2609.30284","doi":"https://doi.org/10.48550/arxiv.2609.30284","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.30284","pdf_url":null,"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,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.30284","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.30284","pdf_url":"https://arxiv.org/pdf/2609.30284","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,"listed_in":[],"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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3955724869","display_name":null,"funder_award_id":"11921005","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7598817452","display_name":null,"funder_award_id":"92365202","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7778110269","display_name":null,"funder_award_id":"12475011","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214671192.pdf","grobid_xml":"https://content.openalex.org/works/W7214671192.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7163379674"],"related_works":["https://openalex.org/W2073883282","https://openalex.org/W2896586776","https://openalex.org/W2153694475","https://openalex.org/W2992732403","https://openalex.org/W3007900298","https://openalex.org/W2035544568","https://openalex.org/W7214108587","https://openalex.org/W287364874","https://openalex.org/W310052026","https://openalex.org/W2140915619"],"abstract_inverted_index":{"Von":[0],"Neumann":[1,33],"proposed":[2],"two":[3],"quantum":[4,21,96],"entropies,":[5,65],"one":[6],"in":[7,12,23],"1927":[8,27,70],"and":[9,61,76],"the":[10,30,59,69,87,91],"other":[11],"1929.":[13],"He":[14],"intended":[15],"to":[16],"define":[17],"thermodynamic":[18,74,93],"entropy":[19,28,71,75,89,94],"for":[20,38,48,95],"states":[22],"both":[24,64],"cases.":[25],"The":[26,42],"is":[29,36,46,72,90],"well-known":[31],"von":[32],"entropy,":[34,44],"which":[35,45],"zero":[37],"all":[39,50],"pure":[40,51],"states.":[41,97],"1929":[43,88],"nonzero":[47],"almost":[49],"states,":[52],"has":[53],"largely":[54],"been":[55],"ignored.":[56],"After":[57],"reviewing":[58],"history":[60],"properties":[62],"of":[63,84],"we":[66],"argue":[67],"that":[68],"not":[73],"should":[77],"be":[78],"used":[79],"simply":[80],"as":[81],"a":[82],"measure":[83],"entanglement,":[85],"whereas":[86],"true":[92]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-29T00:00:00"}