{"id":"https://openalex.org/W2980871861","doi":"https://doi.org/10.3390/e21101020","title":"Quasi-Entropies and Non-Markovianity","display_name":"Quasi-Entropies and Non-Markovianity","publication_year":2019,"publication_date":"2019-10-21","ids":{"openalex":"https://openalex.org/W2980871861","doi":"https://doi.org/10.3390/e21101020","mag":"2980871861"},"language":"en","primary_location":{"id":"doi:10.3390/e21101020","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21101020","pdf_url":"https://www.mdpi.com/1099-4300/21/10/1020/pdf?version=1571653467","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"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/21/10/1020/pdf?version=1571653467","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050154603","display_name":"Fabio Benatti","orcid":"https://orcid.org/0000-0002-0712-2057"},"institutions":[{"id":"https://openalex.org/I142444530","display_name":"University of Trieste","ror":"https://ror.org/02n742c10","country_code":"IT","type":"education","lineage":["https://openalex.org/I142444530"]},{"id":"https://openalex.org/I4210151851","display_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Trieste","ror":"https://ror.org/05j3snm48","country_code":"IT","type":"facility","lineage":["https://openalex.org/I160013858","https://openalex.org/I4210151851"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Fabio Benatti","raw_affiliation_strings":["Department of Physics, University of Trieste, Strada Costiera 11, I-34151 Trieste, Italy","Istituto Nazionale di Fisica Nucleare (INFN), I-34151 Trieste, Italy"],"raw_orcid":"https://orcid.org/0000-0002-0712-2057","affiliations":[{"raw_affiliation_string":"Department of Physics, University of Trieste, Strada Costiera 11, I-34151 Trieste, Italy","institution_ids":["https://openalex.org/I142444530"]},{"raw_affiliation_string":"Istituto Nazionale di Fisica Nucleare (INFN), I-34151 Trieste, Italy","institution_ids":["https://openalex.org/I4210151851"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032485720","display_name":"Luigi Brancati","orcid":"https://orcid.org/0000-0002-6000-4308"},"institutions":[{"id":"https://openalex.org/I142444530","display_name":"University of Trieste","ror":"https://ror.org/02n742c10","country_code":"IT","type":"education","lineage":["https://openalex.org/I142444530"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Luigi Brancati","raw_affiliation_strings":["Department of Physics, University of Trieste, Strada Costiera 11, I-34151 Trieste, Italy"],"raw_orcid":"https://orcid.org/0000-0002-6000-4308","affiliations":[{"raw_affiliation_string":"Department of Physics, University of Trieste, Strada Costiera 11, I-34151 Trieste, Italy","institution_ids":["https://openalex.org/I142444530"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5050154603"],"corresponding_institution_ids":["https://openalex.org/I142444530","https://openalex.org/I4210151851"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.2891,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.67492149,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"21","issue":"10","first_page":"1020","last_page":"1020"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9991000294685364,"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"}},"topics":[{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9991000294685364,"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"}},{"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"}},{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9983000159263611,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/qubit","display_name":"Qubit","score":0.8413567543029785},{"id":"https://openalex.org/keywords/dissipative-system","display_name":"Dissipative system","score":0.6896353363990784},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5928562879562378},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5343056917190552},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.4955698251724243},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.45163071155548096},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.37355440855026245},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3079359531402588},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.29965686798095703},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.17975753545761108},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.14446929097175598},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06415867805480957}],"concepts":[{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.8413567543029785},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.6896353363990784},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5928562879562378},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5343056917190552},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.4955698251724243},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.45163071155548096},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.37355440855026245},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3079359531402588},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.29965686798095703},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.17975753545761108},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.14446929097175598},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06415867805480957},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e21101020","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21101020","pdf_url":"https://www.mdpi.com/1099-4300/21/10/1020/pdf?version=1571653467","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":"pmh:oai:arts.units.it:11368/2952582","is_oa":true,"landing_page_url":"http://hdl.handle.net/11368/2952582","pdf_url":null,"source":{"id":"https://openalex.org/S4306400480","display_name":"ArTS Archivio della ricerca di Trieste (University of Trieste https://www.units.it/)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142444530","host_organization_name":"University of Trieste","host_organization_lineage":["https://openalex.org/I142444530"],"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":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:9e6715549f6c44fcb2dc0b5d5942b474","is_oa":true,"landing_page_url":"https://doaj.org/article/9e6715549f6c44fcb2dc0b5d5942b474","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 21, Iss 10, p 1020 (2019)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/21/10/1020/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e21101020","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","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7514241","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7514241","pdf_url":null,"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"}],"best_oa_location":{"id":"doi:10.3390/e21101020","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21101020","pdf_url":"https://www.mdpi.com/1099-4300/21/10/1020/pdf?version=1571653467","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":[{"display_name":"Reduced inequalities","score":0.5099999904632568,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2980871861.pdf","grobid_xml":"https://content.openalex.org/works/W2980871861.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W61423009","https://openalex.org/W653474616","https://openalex.org/W1047920659","https://openalex.org/W1482224246","https://openalex.org/W1578322733","https://openalex.org/W1671143355","https://openalex.org/W1973479161","https://openalex.org/W1975677983","https://openalex.org/W1984973950","https://openalex.org/W1992045768","https://openalex.org/W2004980778","https://openalex.org/W2015683881","https://openalex.org/W2032839191","https://openalex.org/W2044421213","https://openalex.org/W2044943649","https://openalex.org/W2046908285","https://openalex.org/W2052344514","https://openalex.org/W2064061733","https://openalex.org/W2068496619","https://openalex.org/W2138828824","https://openalex.org/W2144126354","https://openalex.org/W2160505036","https://openalex.org/W2203720464","https://openalex.org/W2210733279","https://openalex.org/W2340016198","https://openalex.org/W2536721440","https://openalex.org/W2769928476","https://openalex.org/W2795883730","https://openalex.org/W3023466231","https://openalex.org/W3104029636","https://openalex.org/W3105484737","https://openalex.org/W3106147254","https://openalex.org/W3106269494","https://openalex.org/W3122850579","https://openalex.org/W4301874609","https://openalex.org/W6627002732"],"related_works":["https://openalex.org/W2072297803","https://openalex.org/W2012012474","https://openalex.org/W2103410878","https://openalex.org/W3122816630","https://openalex.org/W2055610766","https://openalex.org/W3162077676","https://openalex.org/W3015500497","https://openalex.org/W2797511005","https://openalex.org/W2829662890","https://openalex.org/W1972374761"],"abstract_inverted_index":{"We":[0,58],"address":[1],"an":[2],"informational":[3],"puzzle":[4,61],"that":[5,31],"appears":[6],"with":[7],"a":[8,26],"non-Markovian":[9],"open":[10],"qubit":[11,28],"dynamics:":[12],"namely":[13],"the":[14,20,55,60,64,68],"fact":[15],"that,":[16],"while,":[17],"according":[18],"to":[19,39,67],"existing":[21],"witnesses":[22,70],"of":[23,71],"information":[24,37,50,72],"flows,":[25],"single":[27],"affected":[29],"by":[30,62],"dissipative":[32],"dynamics":[33],"does":[34],"not":[35],"show":[36,48],"returning":[38],"it":[40],"from":[41],"its":[42],"environment,":[43],"instead":[44],"two":[45],"qubits":[46],"do":[47],"such":[49],"when":[51],"evolving":[52],"independently":[53],"under":[54],"same":[56],"dynamics.":[57],"solve":[59],"adding":[63],"so-called":[65],"quasi-entropies":[66],"possible":[69],"flows.":[73]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2}],"updated_date":"2026-06-06T09:05:17.133730","created_date":"2025-10-10T00:00:00"}