{"id":"https://openalex.org/W4391476813","doi":"https://doi.org/10.1142/s123016122350018x","title":"Thermodynamic Formalism for Continuous-Time Quantum Markov Semigroups: the Detailed Balance Condition, Entropy, Pressure and Equilibrium Quantum Processes","display_name":"Thermodynamic Formalism for Continuous-Time Quantum Markov Semigroups: the Detailed Balance Condition, Entropy, Pressure and Equilibrium Quantum Processes","publication_year":2023,"publication_date":"2023-12-01","ids":{"openalex":"https://openalex.org/W4391476813","doi":"https://doi.org/10.1142/s123016122350018x"},"language":"en","primary_location":{"id":"doi:10.1142/s123016122350018x","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1142/s123016122350018x","pdf_url":null,"source":{"id":"https://openalex.org/S27332288","display_name":"Open Systems & Information Dynamics","issn_l":"1230-1612","issn":["1230-1612","1573-1324","1793-7191"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Open Systems & Information Dynamics","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/A5089393248","display_name":"Jader E. Brasil","orcid":null},"institutions":[{"id":"https://openalex.org/I130442723","display_name":"Universidade Federal do Rio Grande do Sul","ror":"https://ror.org/041yk2d64","country_code":"BR","type":"education","lineage":["https://openalex.org/I130442723"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Jader E. Brasil","raw_affiliation_strings":["IME\u2013UFRGS, Porto Alegre, Brazil"],"affiliations":[{"raw_affiliation_string":"IME\u2013UFRGS, Porto Alegre, Brazil","institution_ids":["https://openalex.org/I130442723"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090930875","display_name":"Josu\u00e9 Knorst","orcid":"https://orcid.org/0000-0002-2185-529X"},"institutions":[{"id":"https://openalex.org/I130442723","display_name":"Universidade Federal do Rio Grande do Sul","ror":"https://ror.org/041yk2d64","country_code":"BR","type":"education","lineage":["https://openalex.org/I130442723"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Josu\u00e9 Knorst","raw_affiliation_strings":["IME\u2013UFRGS, Porto Alegre, Brazil"],"affiliations":[{"raw_affiliation_string":"IME\u2013UFRGS, Porto Alegre, Brazil","institution_ids":["https://openalex.org/I130442723"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062442811","display_name":"Artur O. Lopes","orcid":"https://orcid.org/0000-0003-2040-4603"},"institutions":[{"id":"https://openalex.org/I130442723","display_name":"Universidade Federal do Rio Grande do Sul","ror":"https://ror.org/041yk2d64","country_code":"BR","type":"education","lineage":["https://openalex.org/I130442723"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Artur O. Lopes","raw_affiliation_strings":["IME\u2013UFRGS, Porto Alegre, Brazil"],"affiliations":[{"raw_affiliation_string":"IME\u2013UFRGS, Porto Alegre, Brazil","institution_ids":["https://openalex.org/I130442723"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5089393248"],"corresponding_institution_ids":["https://openalex.org/I130442723"],"apc_list":null,"apc_paid":null,"fwci":0.1667,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.49006589,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"30","issue":"04","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9998000264167786,"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9998000264167786,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.992900013923645,"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/detailed-balance","display_name":"Detailed balance","score":0.6931424140930176},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.6613049507141113},{"id":"https://openalex.org/keywords/formalism","display_name":"Formalism (music)","score":0.5678132772445679},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5441218614578247},{"id":"https://openalex.org/keywords/balance-equation","display_name":"Balance equation","score":0.5157127976417542},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4487886130809784},{"id":"https://openalex.org/keywords/time-evolution","display_name":"Time evolution","score":0.4309682846069336},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4304325580596924},{"id":"https://openalex.org/keywords/quantum-discord","display_name":"Quantum discord","score":0.42479902505874634},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.42408913373947144},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.4092106819152832},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.27060821652412415},{"id":"https://openalex.org/keywords/open-quantum-system","display_name":"Open quantum system","score":0.26662272214889526},{"id":"https://openalex.org/keywords/markov-model","display_name":"Markov model","score":0.1880340576171875}],"concepts":[{"id":"https://openalex.org/C135694725","wikidata":"https://www.wikidata.org/wiki/Q1201087","display_name":"Detailed balance","level":2,"score":0.6931424140930176},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.6613049507141113},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.5678132772445679},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5441218614578247},{"id":"https://openalex.org/C158917313","wikidata":"https://www.wikidata.org/wiki/Q4849964","display_name":"Balance equation","level":4,"score":0.5157127976417542},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4487886130809784},{"id":"https://openalex.org/C106553664","wikidata":"https://www.wikidata.org/wiki/Q1156744","display_name":"Time evolution","level":2,"score":0.4309682846069336},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4304325580596924},{"id":"https://openalex.org/C139356082","wikidata":"https://www.wikidata.org/wiki/Q7269038","display_name":"Quantum discord","level":4,"score":0.42479902505874634},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.42408913373947144},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.4092106819152832},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.27060821652412415},{"id":"https://openalex.org/C190474826","wikidata":"https://www.wikidata.org/wiki/Q2495111","display_name":"Open quantum system","level":3,"score":0.26662272214889526},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.1880340576171875},{"id":"https://openalex.org/C558565934","wikidata":"https://www.wikidata.org/wiki/Q2743","display_name":"Musical","level":2,"score":0.0},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s123016122350018x","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1142/s123016122350018x","pdf_url":null,"source":{"id":"https://openalex.org/S27332288","display_name":"Open Systems & Information Dynamics","issn_l":"1230-1612","issn":["1230-1612","1573-1324","1793-7191"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Open Systems & Information Dynamics","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":11,"referenced_works":["https://openalex.org/W1548798610","https://openalex.org/W1554869488","https://openalex.org/W2004678689","https://openalex.org/W2121049537","https://openalex.org/W2136139959","https://openalex.org/W2155659639","https://openalex.org/W2963656694","https://openalex.org/W3101329361","https://openalex.org/W3102558967","https://openalex.org/W3103453693","https://openalex.org/W3105760551"],"related_works":["https://openalex.org/W2198039967","https://openalex.org/W2172129038","https://openalex.org/W4388327383","https://openalex.org/W2114546794","https://openalex.org/W2791126921","https://openalex.org/W2921825558","https://openalex.org/W3011478189","https://openalex.org/W1520372854","https://openalex.org/W2049761345","https://openalex.org/W2741006595"],"abstract_inverted_index":{"Let":[0],"[Formula:":[1,8,12,22,25,29,40,46,49,61,69,72,87,90,99,117,124,146,152,165,175,189,192,214,230],"see":[2,9,13,23,26,30,41,47,50,62,70,73,88,91,100,118,125,147,153,166,176,190,193,215,231],"text]":[3,10,14,31,51,92,126,154,167],"denote":[4],"the":[5,33,65,129,140,179,187,204,212,220,225,228],"set":[6],"of":[7,108,113,131,139,143,227],"by":[11,86,186],"complex":[15],"matrices.":[16],"Consider":[17],"continuous":[18,79,180,205],"time":[19,80,181,206],"quantum":[20,53,66,82,182,208,221],"semigroups":[21],"text],":[24,27,42,48,63,71,74,89,101,191,194],"where":[28],"is":[32],"infinitesimal":[34,173],"generator.":[35],"If":[36],"we":[37,43,75,102,134,168],"assume":[38],"that":[39],"will":[44,103,135,157,169,201],"call":[45],"a":[52,57,78,95,105,111,121,132,137,171],"Markov":[54,67,83,183,209],"semigroup.":[55],"Given":[56,93,120],"stationary":[58,81,198],"density":[59,114,150,162,199],"matrix":[60,151],"for":[64,110,145,211,224],"semigroup":[68,188],"can":[76],"define":[77],"process,":[84],"denoted":[85],"an":[94,160,196],"priori":[96],"Laplacian":[97],"operator":[98,123],"present":[104],"natural":[106],"concept":[107],"entropy":[109],"class":[112],"matrices":[115],"on":[116],"text].":[119,148,177,216,232],"Hermitian":[122],"(which":[127],"plays":[128],"role":[130],"Hamiltonian),":[133],"study":[136],"version":[138],"variational":[141],"principle":[142],"pressure":[144,156],"A":[149],"maximizing":[155],"be":[158,202],"called":[159,203],"equilibrium":[161,207,223],"matrix.":[163],"From":[164],"derive":[170],"new":[172],"generator":[174],"Finally,":[178],"process":[184,210],"defined":[185],"and":[195],"initial":[197],"matrix,":[200],"Hamiltonian":[213,229],"It":[217],"corresponds":[218],"to":[219],"thermodynamical":[222],"action":[226]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2025-12-25T23:11:45.687758","created_date":"2025-10-10T00:00:00"}