{"id":"https://openalex.org/W4396232268","doi":"https://doi.org/10.3390/e26050367","title":"Canonical vs. Grand Canonical Ensemble for Bosonic Gases under Harmonic Confinement","display_name":"Canonical vs. Grand Canonical Ensemble for Bosonic Gases under Harmonic Confinement","publication_year":2024,"publication_date":"2024-04-26","ids":{"openalex":"https://openalex.org/W4396232268","doi":"https://doi.org/10.3390/e26050367","pmid":"https://pubmed.ncbi.nlm.nih.gov/38785616"},"language":"en","primary_location":{"id":"doi:10.3390/e26050367","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26050367","pdf_url":"https://www.mdpi.com/1099-4300/26/5/367/pdf","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":["arxiv","crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/26/5/367/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034553663","display_name":"A. Crisanti","orcid":"https://orcid.org/0000-0002-9869-4420"},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Andrea Crisanti","raw_affiliation_strings":["Dipartimento di Fisica, Universit\u00e0 di Roma \u201cLa Sapienza\u201d, Piazzale Moro 5, 00185 Roma, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Fisica, Universit\u00e0 di Roma \u201cLa Sapienza\u201d, Piazzale Moro 5, 00185 Roma, Italy","institution_ids":["https://openalex.org/I861853513"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045873538","display_name":"Luca Salasnich","orcid":"https://orcid.org/0000-0003-0817-4753"},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]},{"id":"https://openalex.org/I4210105455","display_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Padova","ror":"https://ror.org/00z34yn88","country_code":"IT","type":"facility","lineage":["https://openalex.org/I160013858","https://openalex.org/I4210105455"]},{"id":"https://openalex.org/I4210120496","display_name":"National Institute of Optics","ror":"https://ror.org/02dp3a879","country_code":"IT","type":"facility","lineage":["https://openalex.org/I4210120496","https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Luca Salasnich","raw_affiliation_strings":["Dipartimento di Fisica e Astronomia \u201cGalileo Galilei\u201d and Padua QTech Center, Universit\u00e0 di Padova, Via Marzolo 8, 35131 Padova, Italy","Istituto Nazionale di Fisica Nucleare, Sezione di Padova, Via Marzolo 8, 35131 Padova, Italy","Istituto Nazionale di Ottica del Consiglio Nazionale Delle Ricerche, Via Nello Carrara 2, 50127 Sesto Fiorentino, Italy"],"raw_orcid":"https://orcid.org/0000-0003-0817-4753","affiliations":[{"raw_affiliation_string":"Dipartimento di Fisica e Astronomia \u201cGalileo Galilei\u201d and Padua QTech Center, Universit\u00e0 di Padova, Via Marzolo 8, 35131 Padova, Italy","institution_ids":["https://openalex.org/I138689650"]},{"raw_affiliation_string":"Istituto Nazionale di Fisica Nucleare, Sezione di Padova, Via Marzolo 8, 35131 Padova, Italy","institution_ids":["https://openalex.org/I4210105455"]},{"raw_affiliation_string":"Istituto Nazionale di Ottica del Consiglio Nazionale Delle Ricerche, Via Nello Carrara 2, 50127 Sesto Fiorentino, Italy","institution_ids":["https://openalex.org/I4210120496"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052589783","display_name":"Alessandro Sarracino","orcid":"https://orcid.org/0000-0003-3686-0822"},"institutions":[{"id":"https://openalex.org/I197809005","display_name":"University of Campania \"Luigi Vanvitelli\"","ror":"https://ror.org/02kqnpp86","country_code":"IT","type":"education","lineage":["https://openalex.org/I197809005"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Alessandro Sarracino","raw_affiliation_strings":["Dipartimento di Ingegneria, Universit\u00e0 della Campania \u201cLuigi Vanvitelli\u201d, Via Roma 29, 81031 Aversa, Italy"],"raw_orcid":"https://orcid.org/0000-0003-3686-0822","affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria, Universit\u00e0 della Campania \u201cLuigi Vanvitelli\u201d, Via Roma 29, 81031 Aversa, Italy","institution_ids":["https://openalex.org/I197809005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032378931","display_name":"Marco Zannetti","orcid":null},"institutions":[{"id":"https://openalex.org/I131729948","display_name":"University of Salerno","ror":"https://ror.org/0192m2k53","country_code":"IT","type":"education","lineage":["https://openalex.org/I131729948"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Marco Zannetti","raw_affiliation_strings":["Dipartimento di Fisica \u201cEduardo Caianiello\u201d, Universit\u00e0 di Salerno, Via Giovanni Paolo II 132, 84084 Salerno, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Fisica \u201cEduardo Caianiello\u201d, Universit\u00e0 di Salerno, Via Giovanni Paolo II 132, 84084 Salerno, Italy","institution_ids":["https://openalex.org/I131729948"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.8379,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.69282005,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"26","issue":"5","first_page":"367","last_page":"367"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10425","display_name":"Cold Atom Physics and Bose-Einstein Condensates","score":1.0,"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/T10425","display_name":"Cold Atom Physics and Bose-Einstein Condensates","score":1.0,"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":0.9995999932289124,"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/T11965","display_name":"Quantum, superfluid, helium dynamics","score":0.9990000128746033,"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/grand-canonical-ensemble","display_name":"Grand canonical ensemble","score":0.8360742330551147},{"id":"https://openalex.org/keywords/canonical-ensemble","display_name":"Canonical ensemble","score":0.7735155820846558},{"id":"https://openalex.org/keywords/microcanonical-ensemble","display_name":"Microcanonical ensemble","score":0.7551770806312561},{"id":"https://openalex.org/keywords/thermodynamic-limit","display_name":"Thermodynamic limit","score":0.6524092555046082},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.647644579410553},{"id":"https://openalex.org/keywords/harmonic-oscillator","display_name":"Harmonic oscillator","score":0.5064648389816284},{"id":"https://openalex.org/keywords/formalism","display_name":"Formalism (music)","score":0.4444717466831207},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.42188602685928345},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.4167523682117462},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.19156593084335327}],"concepts":[{"id":"https://openalex.org/C29235156","wikidata":"https://www.wikidata.org/wiki/Q1153553","display_name":"Grand canonical ensemble","level":3,"score":0.8360742330551147},{"id":"https://openalex.org/C28556851","wikidata":"https://www.wikidata.org/wiki/Q1077753","display_name":"Canonical ensemble","level":3,"score":0.7735155820846558},{"id":"https://openalex.org/C101683677","wikidata":"https://www.wikidata.org/wiki/Q1077769","display_name":"Microcanonical ensemble","level":4,"score":0.7551770806312561},{"id":"https://openalex.org/C54021167","wikidata":"https://www.wikidata.org/wiki/Q1103484","display_name":"Thermodynamic limit","level":2,"score":0.6524092555046082},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.647644579410553},{"id":"https://openalex.org/C40934718","wikidata":"https://www.wikidata.org/wiki/Q190070","display_name":"Harmonic oscillator","level":2,"score":0.5064648389816284},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.4444717466831207},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.42188602685928345},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.4167523682117462},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.19156593084335327},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C558565934","wikidata":"https://www.wikidata.org/wiki/Q2743","display_name":"Musical","level":2,"score":0.0},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"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/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3390/e26050367","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26050367","pdf_url":"https://www.mdpi.com/1099-4300/26/5/367/pdf","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:38785616","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/38785616","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:arXiv.org:2404.17300","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2404.17300","pdf_url":"https://arxiv.org/pdf/2404.17300","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:iris.uniroma1.it:11573/1716261","is_oa":true,"landing_page_url":"https://hdl.handle.net/11573/1716261","pdf_url":"https://iris.uniroma1.it/bitstream/11573/1716261/1/Crisanti_Canonical_2024.pdf","source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","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","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:pubmedcentral.nih.gov:11120418","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/11120418","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC11120418/pdf/entropy-26-00367.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:ddf4ce6dead54b8192e6f0f16a3b0cde","is_oa":true,"landing_page_url":"https://doaj.org/article/ddf4ce6dead54b8192e6f0f16a3b0cde","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 26, Iss 5, p 367 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e26050367","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26050367","pdf_url":"https://www.mdpi.com/1099-4300/26/5/367/pdf","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":"Affordable and clean energy","score":0.5899999737739563,"id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321966","display_name":"Universit\u00e0 degli Studi di Padova","ror":"https://ror.org/00240q980"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4396232268.pdf","grobid_xml":"https://content.openalex.org/works/W4396232268.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W1616651418","https://openalex.org/W1932911054","https://openalex.org/W1971154415","https://openalex.org/W1972052468","https://openalex.org/W1979433311","https://openalex.org/W1979700341","https://openalex.org/W1980391910","https://openalex.org/W1991602497","https://openalex.org/W1993525402","https://openalex.org/W2007132916","https://openalex.org/W2014942110","https://openalex.org/W2034012235","https://openalex.org/W2038711283","https://openalex.org/W2060365385","https://openalex.org/W2061432205","https://openalex.org/W2083531734","https://openalex.org/W2088593317","https://openalex.org/W2092159648","https://openalex.org/W2094407181","https://openalex.org/W2103752582","https://openalex.org/W2132639490","https://openalex.org/W2176364383","https://openalex.org/W2339026752","https://openalex.org/W2735922764","https://openalex.org/W2884524542","https://openalex.org/W2953284356","https://openalex.org/W2971809278","https://openalex.org/W3098510416","https://openalex.org/W3102000025","https://openalex.org/W4229495386","https://openalex.org/W4317615568","https://openalex.org/W4391740720"],"related_works":["https://openalex.org/W1987811899","https://openalex.org/W2623986776","https://openalex.org/W3099266664","https://openalex.org/W2070218057","https://openalex.org/W1439275944","https://openalex.org/W1639307663","https://openalex.org/W2148120796","https://openalex.org/W2023796012","https://openalex.org/W2984577500","https://openalex.org/W2725389348"],"abstract_inverted_index":{"We":[0,15,100,128],"analyze":[1],"the":[2,12,35,41,59,64,104,108,114,120,135,153,158],"general":[3],"relation":[4],"between":[5],"canonical":[6,9,60,81,123],"and":[7,32,62,138,141],"grand":[8,80,122],"ensembles":[10,111,156],"in":[11,34,73,95,102,113,157],"thermodynamic":[13,159],"limit.":[14,160],"begin":[16],"our":[17,85],"discussion":[18],"by":[19,30,40,58,63],"deriving,":[20],"with":[21,48,71,144],"an":[22],"alternative":[23],"approach,":[24],"some":[25],"standard":[26],"results":[27],"first":[28],"obtained":[29],"Kac":[31],"coworkers":[33],"late":[36],"1970s.":[37],"Then,":[38],"motivated":[39],"Bose-Einstein":[42],"condensation":[43],"(BEC)":[44],"of":[45,52,69,90,107,110,125,155],"trapped":[46],"gases":[47],"a":[49,74,88,96],"fixed":[50],"number":[51],"atoms,":[53],"which":[54],"is":[55],"well":[56],"described":[57],"ensemble":[61],"recent":[65],"groundbreaking":[66],"experimental":[67,146],"realization":[68],"BEC":[70],"photons":[72],"dye-filled":[75],"optical":[76],"microcavity":[77],"under":[78],"genuine":[79],"conditions,":[82],"we":[83,151],"apply":[84],"formalism":[86],"to":[87,119],"system":[89],"non-interacting":[91],"Bose":[92],"particles":[93],"confined":[94],"two-dimensional":[97],"harmonic":[98],"trap.":[99],"discuss":[101],"detail":[103],"mathematical":[105],"origin":[106],"inequivalence":[109],"observed":[112],"condensed":[115],"phase,":[116],"giving":[117],"place":[118],"so-called":[121],"catastrophe":[124],"density":[126],"fluctuations.":[127],"also":[129],"provide":[130],"explicit":[131],"analytical":[132],"expressions":[133],"for":[134],"internal":[136],"energy":[137],"specific":[139],"heat":[140],"compare":[142],"them":[143],"available":[145],"data.":[147],"For":[148],"these":[149],"quantities,":[150],"show":[152],"equivalence":[154]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2025-10-10T00:00:00"}