{"id":"https://openalex.org/W2996442463","doi":"https://doi.org/10.22331/q-2021-03-15-411","title":"The geometry of passivity for quantum systems and a novel elementary derivation of the Gibbs state","display_name":"The geometry of passivity for quantum systems and a novel elementary derivation of the Gibbs state","publication_year":2021,"publication_date":"2021-03-15","ids":{"openalex":"https://openalex.org/W2996442463","doi":"https://doi.org/10.22331/q-2021-03-15-411","mag":"2996442463"},"language":"en","primary_location":{"id":"doi:10.22331/q-2021-03-15-411","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-03-15-411","pdf_url":"https://quantum-journal.org/papers/q-2021-03-15-411/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2021-03-15-411/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Nikolaos Koukoulekidis","orcid":"https://orcid.org/0000-0003-2717-4505"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Nikolaos Koukoulekidis","raw_affiliation_strings":["Department of Physics, Imperial College London, London SW7 2AZ, UK"],"affiliations":[{"raw_affiliation_string":"Department of Physics, Imperial College London, London SW7 2AZ, UK","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Rhea Alexander","orcid":null},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Rhea Alexander","raw_affiliation_strings":["Department of Physics, Imperial College London, London SW7 2AZ, UK"],"affiliations":[{"raw_affiliation_string":"Department of Physics, Imperial College London, London SW7 2AZ, UK","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Thomas Hebdige","orcid":null},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]},{"id":"https://openalex.org/I52099693","display_name":"University of York","ror":"https://ror.org/04m01e293","country_code":"GB","type":"education","lineage":["https://openalex.org/I52099693"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Thomas Hebdige","raw_affiliation_strings":["Department of Mathematics, University of York, Heslington, York, YO10 5DD, UK","Department of Physics, Imperial College London, London SW7 2AZ, UK"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of York, Heslington, York, YO10 5DD, UK","institution_ids":["https://openalex.org/I52099693"]},{"raw_affiliation_string":"Department of Physics, Imperial College London, London SW7 2AZ, UK","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"last","author":{"id":null,"display_name":"David Jennings","orcid":null},"institutions":[{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]},{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]},{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"David Jennings","raw_affiliation_strings":["Department of Physics, Imperial College London, London SW7 2AZ, UK","Department of Physics, University of Oxford, Oxford, OX1 3PU, UK","School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT, UK"],"affiliations":[{"raw_affiliation_string":"Department of Physics, Imperial College London, London SW7 2AZ, UK","institution_ids":["https://openalex.org/I47508984"]},{"raw_affiliation_string":"Department of Physics, University of Oxford, Oxford, OX1 3PU, UK","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT, UK","institution_ids":["https://openalex.org/I130828816"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I47508984"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":0.9187,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.72689781,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"5","issue":null,"first_page":"411","last_page":"411"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.8294000029563904,"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":0.8294000029563904,"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/T11804","display_name":"Quantum many-body systems","score":0.13259999454021454,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.005100000184029341,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/passivity","display_name":"Passivity","score":0.6504999995231628},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.6269999742507935},{"id":"https://openalex.org/keywords/quantum-system","display_name":"Quantum system","score":0.5936999917030334},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4943999946117401},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.4765999913215637},{"id":"https://openalex.org/keywords/gibbs-state","display_name":"Gibbs state","score":0.4489000141620636},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.43290001153945923},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.4163999855518341}],"concepts":[{"id":"https://openalex.org/C2778809601","wikidata":"https://www.wikidata.org/wiki/Q1045736","display_name":"Passivity","level":2,"score":0.6504999995231628},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.6269999742507935},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.5936999917030334},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4999000132083893},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4943999946117401},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.4765999913215637},{"id":"https://openalex.org/C2780872131","wikidata":"https://www.wikidata.org/wiki/Q5558987","display_name":"Gibbs state","level":3,"score":0.4489000141620636},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.43290001153945923},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4163999855518341},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.40380001068115234},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3977999985218048},{"id":"https://openalex.org/C131157278","wikidata":"https://www.wikidata.org/wiki/Q51363","display_name":"Thermodynamic equilibrium","level":2,"score":0.3894999921321869},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.3864000141620636},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.37599998712539673},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.32420000433921814},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.32359999418258667},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.32199999690055847},{"id":"https://openalex.org/C2776897741","wikidata":"https://www.wikidata.org/wiki/Q12212546","display_name":"Quantum thermodynamics","level":3,"score":0.30570000410079956},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.302700012922287},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2955000102519989},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.29260000586509705},{"id":"https://openalex.org/C14380042","wikidata":"https://www.wikidata.org/wiki/Q503327","display_name":"Thermodynamic system","level":2,"score":0.2847999930381775},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.272599995136261},{"id":"https://openalex.org/C34829970","wikidata":"https://www.wikidata.org/wiki/Q845260","display_name":"Quantum statistical mechanics","level":3,"score":0.26930001378059387},{"id":"https://openalex.org/C110202963","wikidata":"https://www.wikidata.org/wiki/Q1783542","display_name":"Convex geometry","level":5,"score":0.2529999911785126},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2529999911785126}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.22331/q-2021-03-15-411","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-03-15-411","pdf_url":"https://quantum-journal.org/papers/q-2021-03-15-411/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1912.07968","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1912.07968","pdf_url":"https://arxiv.org/pdf/1912.07968","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"pmh:oai:doaj.org/article:7b3be9857b7f4561a4c1567224d1ef1a","is_oa":true,"landing_page_url":"https://doaj.org/article/7b3be9857b7f4561a4c1567224d1ef1a","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, Vol 5, p 411 (2021)","raw_type":"article"},{"id":"pmh:oai:spiral.imperial.ac.uk:10044/1/88377","is_oa":true,"landing_page_url":"http://hdl.handle.net/10044/1/88377","pdf_url":null,"source":{"id":"https://openalex.org/S4306401396","display_name":"Spiral (Imperial College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I47508984","host_organization_name":"Imperial College London","host_organization_lineage":["https://openalex.org/I47508984"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"24","raw_type":"Journal Article"}],"best_oa_location":{"id":"doi:10.22331/q-2021-03-15-411","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-03-15-411","pdf_url":"https://quantum-journal.org/papers/q-2021-03-15-411/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1361938442","display_name":null,"funder_award_id":"Fellowship","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G1459926963","display_name":null,"funder_award_id":"EP/T001011/1.","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G2674840903","display_name":null,"funder_award_id":"Fellowship","funder_id":"https://openalex.org/F4320320006","funder_display_name":"Royal Society"},{"id":"https://openalex.org/G4164594981","display_name":"The EPSRC Quantum Communications Hub","funder_award_id":"EP/T001011/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5288895031","display_name":null,"funder_award_id":"EPSRC Centre for Doctoral Training","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6244725262","display_name":null,"funder_award_id":"Centre for Doctoral Training","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7601986463","display_name":null,"funder_award_id":"EP/V002732/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G87932940","display_name":null,"funder_award_id":"EP/T001011/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320320006","display_name":"Royal Society","ror":"https://ror.org/03wnrjx87"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2996442463.pdf","grobid_xml":"https://content.openalex.org/works/W2996442463.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W1575867504","https://openalex.org/W1658381290","https://openalex.org/W1759597146","https://openalex.org/W2006107912","https://openalex.org/W2011510463","https://openalex.org/W2018484716","https://openalex.org/W2023728433","https://openalex.org/W2029705873","https://openalex.org/W2032558547","https://openalex.org/W2035306310","https://openalex.org/W2063890426","https://openalex.org/W2076977679","https://openalex.org/W2079827145","https://openalex.org/W2114826682","https://openalex.org/W2184417789","https://openalex.org/W2202981123","https://openalex.org/W2267101047","https://openalex.org/W2328860787","https://openalex.org/W2468750585","https://openalex.org/W2470470200","https://openalex.org/W2549063097","https://openalex.org/W2575296663","https://openalex.org/W2725257871","https://openalex.org/W2737556421","https://openalex.org/W2799163295","https://openalex.org/W2911745602","https://openalex.org/W2912209775","https://openalex.org/W2994139539","https://openalex.org/W2994805963","https://openalex.org/W3009453918","https://openalex.org/W3161191222","https://openalex.org/W4206007682","https://openalex.org/W4252028749","https://openalex.org/W4290464992","https://openalex.org/W4292058084","https://openalex.org/W4302327534"],"related_works":[],"abstract_inverted_index":{"Passivity":[0],"is":[1,49],"a":[2,7,20,40,54,106,111,138],"fundamental":[3],"concept":[4],"that":[5,32,116],"constitutes":[6],"necessary":[8],"condition":[9],"for":[10,19,62,92],"any":[11],"quantum":[12,63,94],"system":[13,128],"to":[14,24,43,99,125,146],"attain":[15],"thermodynamic":[16],"equilibrium,":[17],"and":[18,115,149],"notion":[21],"of":[22,74,119,133,142],"temperature":[23],"emerge.":[25],"While":[26],"extensive":[27],"work":[28],"has":[29],"been":[30],"done":[31],"exploits":[33],"this,":[34],"the":[35,44,72,75,117,123,127,131],"transition":[36],"from":[37,78,130],"passivity":[38,61],"at":[39],"single-shot":[41],"level":[42],"completely":[45],"passive":[46,79,101],"Gibbs":[47,76],"state":[48,77],"technically":[50],"clear":[51],"but":[52],"lacks":[53],"good":[55],"over-arching":[56],"intuition.":[57],"Here,":[58],"we":[59],"reformulate":[60],"systems":[64],"in":[65,110],"purely":[66],"geometric":[67,140],"terms.":[68],"This":[69,136],"description":[70],"makes":[71],"emergence":[73],"states":[80],"entirely":[81],"transparent.":[82],"Beyond":[83],"clarifying":[84],"existing":[85],"results,":[86],"it":[87],"also":[88],"provides":[89,137],"novel":[90,139],"analysis":[91],"non-equilibrium":[93],"systems.":[95],"We":[96],"show":[97],"that,":[98],"every":[100],"state,":[102],"one":[103],"can":[104],"associate":[105],"simple":[107],"convex":[108],"shape":[109,121],"<mml:math":[112,150],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mn>2</mml:mn></mml:math>-dimensional":[113],"plane,":[114],"area":[118],"this":[120],"measures":[122],"degree":[124],"which":[126],"deviates":[129],"manifold":[132],"equilibrium":[134],"states.":[135],"measure":[141],"athermality":[143],"with":[144],"relations":[145],"both":[147],"ergotropy":[148],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>\u03b2</mml:mi></mml:math>--athermality.":[151]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2019-12-26T00:00:00"}
