{"id":"https://openalex.org/W4376652638","doi":"https://doi.org/10.3390/e25050788","title":"A Differential-Geometric Approach to Quantum Ignorance Consistent with Entropic Properties of Statistical Mechanics","display_name":"A Differential-Geometric Approach to Quantum Ignorance Consistent with Entropic Properties of Statistical Mechanics","publication_year":2023,"publication_date":"2023-05-12","ids":{"openalex":"https://openalex.org/W4376652638","doi":"https://doi.org/10.3390/e25050788","pmid":"https://pubmed.ncbi.nlm.nih.gov/37238543"},"language":"en","primary_location":{"id":"doi:10.3390/e25050788","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e25050788","pdf_url":"https://www.mdpi.com/1099-4300/25/5/788/pdf?version=1683877495","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/25/5/788/pdf?version=1683877495","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032723537","display_name":"Shannon Ray","orcid":"https://orcid.org/0000-0001-7358-4455"},"institutions":[{"id":"https://openalex.org/I1280414376","display_name":"United States Air Force Research Laboratory","ror":"https://ror.org/02e2egq70","country_code":"US","type":"facility","lineage":["https://openalex.org/I1280414376","https://openalex.org/I1330347796","https://openalex.org/I4210102105","https://openalex.org/I4389425425"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Shannon Ray","raw_affiliation_strings":["Air Force Research Laboratory, Rome, NY 13441, USA","Griffiss Institute, Rome, NY 13441, USA"],"raw_orcid":"https://orcid.org/0000-0001-7358-4455","affiliations":[{"raw_affiliation_string":"Air Force Research Laboratory, Rome, NY 13441, USA","institution_ids":["https://openalex.org/I1280414376"]},{"raw_affiliation_string":"Griffiss Institute, Rome, NY 13441, USA","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072805864","display_name":"Paul M. Alsing","orcid":"https://orcid.org/0000-0003-0467-5200"},"institutions":[{"id":"https://openalex.org/I1280414376","display_name":"United States Air Force Research Laboratory","ror":"https://ror.org/02e2egq70","country_code":"US","type":"facility","lineage":["https://openalex.org/I1280414376","https://openalex.org/I1330347796","https://openalex.org/I4210102105","https://openalex.org/I4389425425"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Paul M. Alsing","raw_affiliation_strings":["Air Force Research Laboratory, Rome, NY 13441, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Air Force Research Laboratory, Rome, NY 13441, USA","institution_ids":["https://openalex.org/I1280414376"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027136097","display_name":"Carlo Cafaro","orcid":"https://orcid.org/0000-0002-4913-7046"},"institutions":[{"id":"https://openalex.org/I90965887","display_name":"SUNY Polytechnic Institute","ror":"https://ror.org/000fxgx19","country_code":"US","type":"education","lineage":["https://openalex.org/I90965887"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Carlo Cafaro","raw_affiliation_strings":["Department of Mathematics and Physics, SUNY Polytechnic Institute, Albany, NY 12203, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Physics, SUNY Polytechnic Institute, Albany, NY 12203, USA","institution_ids":["https://openalex.org/I90965887"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029700182","display_name":"H S. Jacinto","orcid":"https://orcid.org/0000-0002-2737-7110"},"institutions":[{"id":"https://openalex.org/I1280414376","display_name":"United States Air Force Research Laboratory","ror":"https://ror.org/02e2egq70","country_code":"US","type":"facility","lineage":["https://openalex.org/I1280414376","https://openalex.org/I1330347796","https://openalex.org/I4210102105","https://openalex.org/I4389425425"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"H S. Jacinto","raw_affiliation_strings":["Air Force Research Laboratory, Rome, NY 13441, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Air Force Research Laboratory, Rome, NY 13441, USA","institution_ids":["https://openalex.org/I1280414376"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5032723537"],"corresponding_institution_ids":["https://openalex.org/I1280414376"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04487135,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"25","issue":"5","first_page":"788","last_page":"788"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11804","display_name":"Quantum many-body systems","score":0.9995999932289124,"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/T11804","display_name":"Quantum many-body systems","score":0.9995999932289124,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.9993000030517578,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.9990000128746033,"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/ignorance","display_name":"Ignorance","score":0.7195382118225098},{"id":"https://openalex.org/keywords/statistical-mechanics","display_name":"Statistical mechanics","score":0.671122670173645},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.6016225814819336},{"id":"https://openalex.org/keywords/quantum-statistical-mechanics","display_name":"Quantum statistical mechanics","score":0.4841645359992981},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.41954970359802246},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3991694450378418},{"id":"https://openalex.org/keywords/theoretical-physics","display_name":"Theoretical physics","score":0.3573055565357208},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.34731656312942505},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3438226580619812},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.3201172947883606},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.2998236417770386},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.20346567034721375},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.18422931432724}],"concepts":[{"id":"https://openalex.org/C2778732403","wikidata":"https://www.wikidata.org/wiki/Q815577","display_name":"Ignorance","level":2,"score":0.7195382118225098},{"id":"https://openalex.org/C99874945","wikidata":"https://www.wikidata.org/wiki/Q188715","display_name":"Statistical mechanics","level":2,"score":0.671122670173645},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.6016225814819336},{"id":"https://openalex.org/C34829970","wikidata":"https://www.wikidata.org/wiki/Q845260","display_name":"Quantum statistical mechanics","level":3,"score":0.4841645359992981},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.41954970359802246},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3991694450378418},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.3573055565357208},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.34731656312942505},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3438226580619812},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.3201172947883606},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2998236417770386},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.20346567034721375},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.18422931432724}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e25050788","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e25050788","pdf_url":"https://www.mdpi.com/1099-4300/25/5/788/pdf?version=1683877495","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},{"id":"pmid:37238543","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/37238543","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:10217130","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/10217130","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC10217130/pdf/entropy-25-00788.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:2a5b8d6828464f9c9c7e0bbe5102e92e","is_oa":true,"landing_page_url":"https://doaj.org/article/2a5b8d6828464f9c9c7e0bbe5102e92e","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 25, Iss 5, p 788 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/25/5/788/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e25050788","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Entropy; Volume 25; Issue 5; Pages: 788","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e25050788","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e25050788","pdf_url":"https://www.mdpi.com/1099-4300/25/5/788/pdf?version=1683877495","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4376652638.pdf"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W1409569118","https://openalex.org/W1543229415","https://openalex.org/W1680443341","https://openalex.org/W1912516140","https://openalex.org/W1968244844","https://openalex.org/W1983282154","https://openalex.org/W1988155384","https://openalex.org/W2002840675","https://openalex.org/W2012580347","https://openalex.org/W2032558547","https://openalex.org/W2034442087","https://openalex.org/W2094810855","https://openalex.org/W2098572895","https://openalex.org/W2129671152","https://openalex.org/W2300238109","https://openalex.org/W2530057664","https://openalex.org/W2614264617","https://openalex.org/W2756313597","https://openalex.org/W2787850882","https://openalex.org/W2794284702","https://openalex.org/W2923926064","https://openalex.org/W2963504754","https://openalex.org/W3037704082","https://openalex.org/W3045540182","https://openalex.org/W3092535425","https://openalex.org/W3098156575","https://openalex.org/W3103976103","https://openalex.org/W3105398309","https://openalex.org/W3125996603","https://openalex.org/W3209480925","https://openalex.org/W4246756514","https://openalex.org/W4249726483","https://openalex.org/W6633402864"],"related_works":["https://openalex.org/W4213210312","https://openalex.org/W1973792276","https://openalex.org/W1507485682","https://openalex.org/W399180213","https://openalex.org/W1674692623","https://openalex.org/W3042682751","https://openalex.org/W2126551324","https://openalex.org/W2072090188","https://openalex.org/W1525229531","https://openalex.org/W225962251"],"abstract_inverted_index":{"In":[0,55],"this":[1,56],"paper,":[2],"we":[3,42,90,180],"construct":[4],"the":[5,11,32,37,51,58,65,69,79,95,117,125,135,140,144,149,152,158,167,170,177,183,187,212],"metric":[6],"tensor":[7],"and":[8,48,88,127,133,169,204,226],"volume":[9,33,59,107,113,184],"for":[10,176,196,200],"manifold":[12],"of":[13,39,45,53,64,71,85,94,105,111,143,151,214],"purifications":[14,52],"associated":[15],"with":[16,209],"an":[17,102],"arbitrary":[18],"reduced":[19],"density":[20],"operator":[21],"\u03c1S.":[22,54,75,215],"We":[23],"also":[24],"define":[25],"a":[26,62,121,163,206],"quantum":[27],"coarse-graining":[28],"(CG)":[29],"to":[30,109,162,211,221],"study":[31],"where":[34,78],"macrostates":[35,66,110],"are":[36,50,81,219],"manifolds":[38],"purifications,":[40],"which":[41,124],"call":[43],"surfaces":[44],"ignorance":[46],"(SOI),":[47],"microstates":[49],"context,":[57],"functions":[60],"as":[61,148],"multiplicity":[63],"that":[67,182,192],"quantifies":[68],"amount":[70],"information":[72],"missing":[73],"from":[74],"Using":[76],"examples":[77,178],"SOI":[80],"generated":[82],"using":[83],"representations":[84],"SU(2),":[86],"SO(3),":[87],"SO(N),":[89],"show":[91,181],"two":[92,217],"features":[93,218],"CG:":[96],"(1)":[97,175],"A":[98],"system":[99,126,154,168],"beginning":[100],"in":[101,120,123,191],"atypical":[103],"macrostate":[104,119,137,160],"smaller":[106],"evolves":[108],"greater":[112],"until":[114],"it":[115,193],"reaches":[116],"equilibrium":[118,136,159],"process":[122],"environment":[128],"become":[129],"strictly":[130],"more":[131],"entangled,":[132],"(2)":[134],"takes":[138],"up":[139],"vast":[141],"majority":[142],"coarse-grained":[145],"space":[146],"especially":[147],"dimension":[150],"total":[153],"becomes":[155],"large.":[156],"Here,":[157],"corresponds":[161],"maximum":[164],"entanglement":[165],"between":[166],"environment.":[171],"To":[172],"demonstrate":[173],"feature":[174],"considered,":[179],"behaves":[185],"like":[186],"von":[188],"Neumann":[189],"entropy":[190],"is":[194,205],"zero":[195],"pure":[197],"states,":[198,203],"maximal":[199],"maximally":[201],"mixed":[202],"concave":[207],"function":[208],"respect":[210],"purity":[213],"These":[216],"essential":[220],"typicality":[222],"arguments":[223],"regarding":[224],"thermalization":[225],"Boltzmann's":[227],"original":[228],"CG.":[229]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}