{"id":"https://openalex.org/W2959073436","doi":"https://doi.org/10.3390/e21070677","title":"A Review of the Classical Canonical Ensemble Treatment of Newton\u2019s Gravitation","display_name":"A Review of the Classical Canonical Ensemble Treatment of Newton\u2019s Gravitation","publication_year":2019,"publication_date":"2019-07-11","ids":{"openalex":"https://openalex.org/W2959073436","doi":"https://doi.org/10.3390/e21070677","mag":"2959073436","pmid":"https://pubmed.ncbi.nlm.nih.gov/33267391"},"language":"en","primary_location":{"id":"doi:10.3390/e21070677","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21070677","pdf_url":"https://www.mdpi.com/1099-4300/21/7/677/pdf?version=1562840014","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/1099-4300/21/7/677/pdf?version=1562840014","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020020266","display_name":"F. Pennini","orcid":null},"institutions":[{"id":"https://openalex.org/I151201029","display_name":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas","ror":"https://ror.org/03cqe8w59","country_code":"AR","type":"government","lineage":["https://openalex.org/I151201029","https://openalex.org/I4210123736","https://openalex.org/I4387155568"]},{"id":"https://openalex.org/I197025333","display_name":"Universidad Nacional de La Pampa","ror":"https://ror.org/02c21vy68","country_code":"AR","type":"education","lineage":["https://openalex.org/I197025333"]},{"id":"https://openalex.org/I2802166871","display_name":"Universidad Cat\u00f3lica del Norte","ror":"https://ror.org/02akpm128","country_code":"CL","type":"education","lineage":["https://openalex.org/I2802166871"]}],"countries":["AR","CL"],"is_corresponding":true,"raw_author_name":"Flavia Pennini","raw_affiliation_strings":["Consejo Nacional de Investigaciones Cient\u00edficas y Tecnol\u00f3gicas, (IFLP-CCT-CONICET)-C. C. 727, 1900 La Plata, Argentina","Departamento de F\u00edsica, Universidad Cat\u00f3lica del Norte, Av. Angamos 0610, Antofagasta 2340000, Chile","Fac. de C. Exactas-National University La Pampa, Peru y Uruguay, Santa Rosa, La Pampa 6300, Argentina"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Consejo Nacional de Investigaciones Cient\u00edficas y Tecnol\u00f3gicas, (IFLP-CCT-CONICET)-C. C. 727, 1900 La Plata, Argentina","institution_ids":["https://openalex.org/I151201029"]},{"raw_affiliation_string":"Departamento de F\u00edsica, Universidad Cat\u00f3lica del Norte, Av. Angamos 0610, Antofagasta 2340000, Chile","institution_ids":["https://openalex.org/I2802166871"]},{"raw_affiliation_string":"Fac. de C. Exactas-National University La Pampa, Peru y Uruguay, Santa Rosa, La Pampa 6300, Argentina","institution_ids":["https://openalex.org/I197025333"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068204075","display_name":"A. Plastino","orcid":"https://orcid.org/0000-0001-5934-2783"},"institutions":[{"id":"https://openalex.org/I151201029","display_name":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas","ror":"https://ror.org/03cqe8w59","country_code":"AR","type":"government","lineage":["https://openalex.org/I151201029","https://openalex.org/I4210123736","https://openalex.org/I4387155568"]},{"id":"https://openalex.org/I874386039","display_name":"Universidad Nacional de La Plata","ror":"https://ror.org/01tjs6929","country_code":"AR","type":"education","lineage":["https://openalex.org/I874386039"]}],"countries":["AR"],"is_corresponding":false,"raw_author_name":"Angel Plastino","raw_affiliation_strings":["Consejo Nacional de Investigaciones Cient\u00edficas y Tecnol\u00f3gicas, (IFLP-CCT-CONICET)-C. C. 727, 1900 La Plata, Argentina","Departamento de F\u00edsica, Universidad Nacional de La Plata, La Plata 1900, Argentina"],"raw_orcid":"https://orcid.org/0000-0001-5934-2783","affiliations":[{"raw_affiliation_string":"Consejo Nacional de Investigaciones Cient\u00edficas y Tecnol\u00f3gicas, (IFLP-CCT-CONICET)-C. C. 727, 1900 La Plata, Argentina","institution_ids":["https://openalex.org/I151201029"]},{"raw_affiliation_string":"Departamento de F\u00edsica, Universidad Nacional de La Plata, La Plata 1900, Argentina","institution_ids":["https://openalex.org/I874386039"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090859400","display_name":"M. Rocca","orcid":"https://orcid.org/0000-0002-5019-745X"},"institutions":[{"id":"https://openalex.org/I151201029","display_name":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas","ror":"https://ror.org/03cqe8w59","country_code":"AR","type":"government","lineage":["https://openalex.org/I151201029","https://openalex.org/I4210123736","https://openalex.org/I4387155568"]},{"id":"https://openalex.org/I874386039","display_name":"Universidad Nacional de La Plata","ror":"https://ror.org/01tjs6929","country_code":"AR","type":"education","lineage":["https://openalex.org/I874386039"]}],"countries":["AR"],"is_corresponding":false,"raw_author_name":"Mario Rocca","raw_affiliation_strings":["Consejo Nacional de Investigaciones Cient\u00edficas y Tecnol\u00f3gicas, (IFLP-CCT-CONICET)-C. C. 727, 1900 La Plata, Argentina","Departamento de F\u00edsica, Universidad Nacional de La Plata, La Plata 1900, Argentina","Departamento de Matem\u00e1tica, Universidad Nacional de La Plata, La Plata 1900, Argentina"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Consejo Nacional de Investigaciones Cient\u00edficas y Tecnol\u00f3gicas, (IFLP-CCT-CONICET)-C. C. 727, 1900 La Plata, Argentina","institution_ids":["https://openalex.org/I151201029"]},{"raw_affiliation_string":"Departamento de F\u00edsica, Universidad Nacional de La Plata, La Plata 1900, Argentina","institution_ids":["https://openalex.org/I874386039"]},{"raw_affiliation_string":"Departamento de Matem\u00e1tica, Universidad Nacional de La Plata, La Plata 1900, Argentina","institution_ids":["https://openalex.org/I874386039"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055203606","display_name":"G.L. Ferri","orcid":null},"institutions":[{"id":"https://openalex.org/I197025333","display_name":"Universidad Nacional de La Pampa","ror":"https://ror.org/02c21vy68","country_code":"AR","type":"education","lineage":["https://openalex.org/I197025333"]}],"countries":["AR"],"is_corresponding":false,"raw_author_name":"Gustavo Ferri","raw_affiliation_strings":["Fac. de C. Exactas-National University La Pampa, Peru y Uruguay, Santa Rosa, La Pampa 6300, Argentina"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fac. de C. Exactas-National University La Pampa, Peru y Uruguay, Santa Rosa, La Pampa 6300, Argentina","institution_ids":["https://openalex.org/I197025333"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5020020266"],"corresponding_institution_ids":["https://openalex.org/I151201029","https://openalex.org/I197025333","https://openalex.org/I2802166871"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.4921,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.60591502,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"21","issue":"7","first_page":"677","last_page":"677"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","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/T12261","display_name":"Statistical Mechanics and Entropy","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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9886000156402588,"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/T10095","display_name":"Cosmology and Gravitation Theories","score":0.9866999983787537,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"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/canonical-ensemble","display_name":"Canonical ensemble","score":0.6595293283462524},{"id":"https://openalex.org/keywords/partition-function","display_name":"Partition function (quantum field theory)","score":0.6304394006729126},{"id":"https://openalex.org/keywords/gravitation","display_name":"Gravitation","score":0.5830004811286926},{"id":"https://openalex.org/keywords/boltzmann-distribution","display_name":"Boltzmann distribution","score":0.5011029243469238},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4776110351085663},{"id":"https://openalex.org/keywords/statistical-mechanics","display_name":"Statistical mechanics","score":0.4648042917251587},{"id":"https://openalex.org/keywords/boltzmann-constant","display_name":"Boltzmann constant","score":0.45174548029899597},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4514906406402588},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.4513784646987915},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4454520344734192},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.38149768114089966},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3749435842037201},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.31825172901153564},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2058202624320984},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15651753544807434},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.12433558702468872},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.10528740286827087},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10175621509552002},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07955119013786316}],"concepts":[{"id":"https://openalex.org/C28556851","wikidata":"https://www.wikidata.org/wiki/Q1077753","display_name":"Canonical ensemble","level":3,"score":0.6595293283462524},{"id":"https://openalex.org/C2778401447","wikidata":"https://www.wikidata.org/wiki/Q7140637","display_name":"Partition function (quantum field theory)","level":2,"score":0.6304394006729126},{"id":"https://openalex.org/C124017977","wikidata":"https://www.wikidata.org/wiki/Q11412","display_name":"Gravitation","level":2,"score":0.5830004811286926},{"id":"https://openalex.org/C193999330","wikidata":"https://www.wikidata.org/wiki/Q834200","display_name":"Boltzmann distribution","level":2,"score":0.5011029243469238},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4776110351085663},{"id":"https://openalex.org/C99874945","wikidata":"https://www.wikidata.org/wiki/Q188715","display_name":"Statistical mechanics","level":2,"score":0.4648042917251587},{"id":"https://openalex.org/C35304006","wikidata":"https://www.wikidata.org/wiki/Q5962","display_name":"Boltzmann constant","level":2,"score":0.45174548029899597},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4514906406402588},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.4513784646987915},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4454520344734192},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.38149768114089966},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3749435842037201},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.31825172901153564},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2058202624320984},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15651753544807434},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.12433558702468872},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.10528740286827087},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10175621509552002},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07955119013786316}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.3390/e21070677","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21070677","pdf_url":"https://www.mdpi.com/1099-4300/21/7/677/pdf?version=1562840014","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:33267391","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33267391","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:sedici.unlp.edu.ar:10915/123409","is_oa":true,"landing_page_url":"http://sedici.unlp.edu.ar/handle/10915/123409","pdf_url":"http://sedici.unlp.edu.ar/handle/10915/123409","source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"reponame:SEDICI (UNLP)","raw_type":"http://purl.org/coar/resource_type/c_6501"},{"id":"pmh:oai:doaj.org/article:a48f573bcd4a4deb9d5742b9fd887e5f","is_oa":true,"landing_page_url":"https://doaj.org/article/a48f573bcd4a4deb9d5742b9fd887e5f","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 7, p 677 (2019)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/21/7/677/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e21070677","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:7515174","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7515174","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"},{"id":"pmh:oai:ri.conicet.gov.ar:11336/129854","is_oa":true,"landing_page_url":"http://hdl.handle.net/11336/129854","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"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":"reponame:CONICET Digital (CONICET)","raw_type":"http://purl.org/coar/resource_type/c_6501"}],"best_oa_location":{"id":"doi:10.3390/e21070677","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21070677","pdf_url":"https://www.mdpi.com/1099-4300/21/7/677/pdf?version=1562840014","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":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2959073436.pdf","grobid_xml":"https://content.openalex.org/works/W2959073436.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W982410844","https://openalex.org/W1490039160","https://openalex.org/W1531588570","https://openalex.org/W1568204338","https://openalex.org/W1581504038","https://openalex.org/W1967415215","https://openalex.org/W1972292127","https://openalex.org/W1985436642","https://openalex.org/W1986348618","https://openalex.org/W2009746734","https://openalex.org/W2050747421","https://openalex.org/W2061382758","https://openalex.org/W2061391797","https://openalex.org/W2074334204","https://openalex.org/W2154858141","https://openalex.org/W2155301510","https://openalex.org/W2157005274","https://openalex.org/W2203635712","https://openalex.org/W2749019455","https://openalex.org/W2782826407","https://openalex.org/W2791596609","https://openalex.org/W3022969715","https://openalex.org/W3103940371","https://openalex.org/W3105250981","https://openalex.org/W3106429922"],"related_works":["https://openalex.org/W4383426484","https://openalex.org/W1592374086","https://openalex.org/W4386783530","https://openalex.org/W2510367851","https://openalex.org/W4298123111","https://openalex.org/W3022711213","https://openalex.org/W2558551099","https://openalex.org/W4386784508","https://openalex.org/W4206034251","https://openalex.org/W2048244686"],"abstract_inverted_index":{"It":[0],"is":[1,53],"common":[2],"lore":[3],"that":[4],"the":[5,13,57,68],"canonical":[6],"gravitational":[7],"partition":[8],"function":[9],"Z":[10,33],"associated":[11],"with":[12],"classical":[14],"Boltzmann-Gibbs":[15],"(BG)":[16],"exponential":[17],"distribution":[18],"cannot":[19],"be":[20],"built":[21],"up":[22,32],"because":[23],"of":[24,49,62],"mathematical":[25],"pitfalls.":[26],"The":[27],"integral":[28],"needed":[29],"for":[30],"writing":[31],"diverges.":[34],"We":[35],"review":[36],"here":[37],"how":[38],"to":[39],"avoid":[40],"this":[41],"pitfall":[42],"and":[43,64,66],"obtain":[44],"a":[45],"(classical)":[46],"statistical":[47],"mechanics":[48],"Newton's":[50],"gravitation.":[51],"This":[52],"done":[54],"using":[55],"(1)":[56],"analytical":[58],"extension":[59],"treatment":[60],"obtained":[61],"Gradshteyn":[63],"Rizhik":[65],"(2)":[67],"well":[69],"known":[70],"dimensional":[71],"regularization":[72],"technique.":[73]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
