{"id":"https://openalex.org/W2737147392","doi":"https://doi.org/10.3390/e19080381","title":"Kinetic Theory beyond the Stosszahlansatz","display_name":"Kinetic Theory beyond the Stosszahlansatz","publication_year":2017,"publication_date":"2017-07-25","ids":{"openalex":"https://openalex.org/W2737147392","doi":"https://doi.org/10.3390/e19080381","mag":"2737147392"},"language":"en","primary_location":{"id":"doi:10.3390/e19080381","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e19080381","pdf_url":"https://www.mdpi.com/1099-4300/19/8/381/pdf?version=1500973191","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/1099-4300/19/8/381/pdf?version=1500973191","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085909827","display_name":"Gregor Chliamovitch","orcid":null},"institutions":[{"id":"https://openalex.org/I114457229","display_name":"University of Geneva","ror":"https://ror.org/01swzsf04","country_code":"CH","type":"education","lineage":["https://openalex.org/I114457229"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Gregor Chliamovitch","raw_affiliation_strings":["Department of Computer Science, University of Geneva, Route de Drize 7, 1227 Geneva, Switzerland","Department of Theoretical Physics, University of Geneva, Quai Ernest-Ansermet 24, 1211 Geneva, Switzerland"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Geneva, Route de Drize 7, 1227 Geneva, Switzerland","institution_ids":["https://openalex.org/I114457229"]},{"raw_affiliation_string":"Department of Theoretical Physics, University of Geneva, Quai Ernest-Ansermet 24, 1211 Geneva, Switzerland","institution_ids":["https://openalex.org/I114457229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014617340","display_name":"Orestis Malaspinas","orcid":"https://orcid.org/0000-0001-9427-6849"},"institutions":[{"id":"https://openalex.org/I114457229","display_name":"University of Geneva","ror":"https://ror.org/01swzsf04","country_code":"CH","type":"education","lineage":["https://openalex.org/I114457229"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Orestis Malaspinas","raw_affiliation_strings":["Department of Computer Science, University of Geneva, Route de Drize 7, 1227 Geneva, Switzerland"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Geneva, Route de Drize 7, 1227 Geneva, Switzerland","institution_ids":["https://openalex.org/I114457229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025249509","display_name":"Bastien Chopard","orcid":"https://orcid.org/0000-0002-6638-0945"},"institutions":[{"id":"https://openalex.org/I114457229","display_name":"University of Geneva","ror":"https://ror.org/01swzsf04","country_code":"CH","type":"education","lineage":["https://openalex.org/I114457229"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Bastien Chopard","raw_affiliation_strings":["Department of Computer Science, University of Geneva, Route de Drize 7, 1227 Geneva, Switzerland"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Geneva, Route de Drize 7, 1227 Geneva, Switzerland","institution_ids":["https://openalex.org/I114457229"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5085909827"],"corresponding_institution_ids":["https://openalex.org/I114457229"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.5246,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.64168766,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"19","issue":"8","first_page":"381","last_page":"381"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9995999932289124,"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"}},"topics":[{"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9994000196456909,"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/T12350","display_name":"Particle Dynamics in Fluid Flows","score":0.9728999733924866,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean 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/kinetic-energy","display_name":"Kinetic energy","score":0.6725295782089233},{"id":"https://openalex.org/keywords/distribution-function","display_name":"Distribution function","score":0.6191009283065796},{"id":"https://openalex.org/keywords/boltzmann-constant","display_name":"Boltzmann constant","score":0.6142486929893494},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.606885552406311},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5938844084739685},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.569872260093689},{"id":"https://openalex.org/keywords/kinetic-theory","display_name":"Kinetic theory","score":0.569347620010376},{"id":"https://openalex.org/keywords/boltzmann-equation","display_name":"Boltzmann equation","score":0.5602070689201355},{"id":"https://openalex.org/keywords/momentum","display_name":"Momentum (technical analysis)","score":0.5055363178253174},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4862893521785736},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.46447622776031494},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.41766831278800964},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3699261546134949},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3027835488319397},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.2390468716621399},{"id":"https://openalex.org/keywords/theoretical-physics","display_name":"Theoretical physics","score":0.23498785495758057},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15965363383293152}],"concepts":[{"id":"https://openalex.org/C135889238","wikidata":"https://www.wikidata.org/wiki/Q46276","display_name":"Kinetic energy","level":2,"score":0.6725295782089233},{"id":"https://openalex.org/C186603090","wikidata":"https://www.wikidata.org/wiki/Q55505926","display_name":"Distribution function","level":2,"score":0.6191009283065796},{"id":"https://openalex.org/C35304006","wikidata":"https://www.wikidata.org/wiki/Q5962","display_name":"Boltzmann constant","level":2,"score":0.6142486929893494},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.606885552406311},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5938844084739685},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.569872260093689},{"id":"https://openalex.org/C19979193","wikidata":"https://www.wikidata.org/wiki/Q25100325","display_name":"Kinetic theory","level":2,"score":0.569347620010376},{"id":"https://openalex.org/C165995430","wikidata":"https://www.wikidata.org/wiki/Q891653","display_name":"Boltzmann equation","level":2,"score":0.5602070689201355},{"id":"https://openalex.org/C60718061","wikidata":"https://www.wikidata.org/wiki/Q1414747","display_name":"Momentum (technical analysis)","level":2,"score":0.5055363178253174},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4862893521785736},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.46447622776031494},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.41766831278800964},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3699261546134949},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3027835488319397},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2390468716621399},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.23498785495758057},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15965363383293152},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e19080381","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e19080381","pdf_url":"https://www.mdpi.com/1099-4300/19/8/381/pdf?version=1500973191","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:unige.ch:unige:135931","is_oa":true,"landing_page_url":"https://archive-ouverte.unige.ch/unige:135931","pdf_url":null,"source":{"id":"https://openalex.org/S4306402259","display_name":"Archive ouverte UNIGE (University of Geneva)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I114457229","host_organization_name":"University of Geneva","host_organization_lineage":["https://openalex.org/I114457229"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ISSN: 1099-4300","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:91dbfeb26e2d441f9bbd4aadf08a71cb","is_oa":true,"landing_page_url":"https://doaj.org/article/91dbfeb26e2d441f9bbd4aadf08a71cb","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":"Entropy, Vol 19, Iss 8, p 381 (2017)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/19/8/381/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e19080381","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; Volume 19; Issue 8; Pages: 381","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e19080381","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e19080381","pdf_url":"https://www.mdpi.com/1099-4300/19/8/381/pdf?version=1500973191","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":[{"score":0.8100000023841858,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2737147392.pdf","grobid_xml":"https://content.openalex.org/works/W2737147392.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1569645746","https://openalex.org/W1927690731","https://openalex.org/W1954414299","https://openalex.org/W2018490621","https://openalex.org/W2032558547","https://openalex.org/W2077881080","https://openalex.org/W2092685486","https://openalex.org/W2147238273","https://openalex.org/W2155572780","https://openalex.org/W2581601659","https://openalex.org/W4299551239"],"related_works":["https://openalex.org/W4238782814","https://openalex.org/W58974396","https://openalex.org/W3008020270","https://openalex.org/W4388401275","https://openalex.org/W1577276783","https://openalex.org/W2035883894","https://openalex.org/W2283973112","https://openalex.org/W4388295539","https://openalex.org/W2903553991","https://openalex.org/W2155117438"],"abstract_inverted_index":{"In":[0],"a":[1,53,59,101],"recent":[2],"paper":[3],"(Chliamovitch,":[4],"et":[5],"al.,":[6],"2015),":[7],"we":[8,45,56,72],"suggested":[9],"using":[10],"the":[11,36,40,50,74,81,88,98],"principle":[12],"of":[13,27,35,52,83,90,100],"maximum":[14],"entropy":[15],"to":[16,20,31],"generalize":[17],"Boltzmann\u2019s":[18],"Stosszahlansatz":[19],"higher-order":[21],"distribution":[22,42],"functions.":[23],"This":[24,78],"conceptual":[25],"shift":[26],"focus":[28],"allowed":[29],"us":[30],"derive":[32],"an":[33],"analog":[34],"Boltzmann":[37],"equation":[38],"for":[39,80,97],"two-particle":[41,75],"function.":[43],"While":[44],"only":[46],"briefly":[47],"mentioned":[48],"there":[49],"possibility":[51],"hydrodynamical":[54],"treatment,":[55],"complete":[57],"here":[58],"crucial":[60],"step":[61],"towards":[62],"this":[63],"program.":[64],"We":[65],"discuss":[66],"bilocal":[67],"collisional":[68],"invariants,":[69],"from":[70],"which":[71,87],"deduce":[73],"stationary":[76],"distribution.":[77],"allows":[79],"existence":[82,99],"equilibrium":[84],"states":[85],"in":[86],"momenta":[89],"particles":[91],"are":[92],"correlated,":[93],"as":[94,96],"well":[95],"fourth":[102],"conserved":[103],"quantity":[104],"besides":[105],"mass,":[106],"momentum":[107],"and":[108],"kinetic":[109],"energy.":[110]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2017-07-31T00:00:00"}