{"id":"https://openalex.org/W7207829101","doi":"https://doi.org/10.48550/arxiv.2609.01753","title":"The entropy production is not always monotone for hard spheres or for Maxwell molecules","display_name":"The entropy production is not always monotone for hard spheres or for Maxwell molecules","publication_year":2026,"publication_date":"2026-09-01","ids":{"openalex":"https://openalex.org/W7207829101","doi":"https://doi.org/10.48550/arxiv.2609.01753"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.01753","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01753","pdf_url":"https://arxiv.org/pdf/2609.01753","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.01753","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064604074","display_name":"Luis S. Silvestre Jr","orcid":"https://orcid.org/0009-0003-3564-691X","observed_orcids":["https://orcid.org/0009-0003-3564-691X"]},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Silvestre, Luis","raw_affiliation_strings":["Mathematics Department , University of Chicago , Chicago , IL 60637 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department , University of Chicago , Chicago , IL 60637 , USA","institution_ids":["https://openalex.org/I40347166"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5064604074"],"corresponding_institution_ids":["https://openalex.org/I40347166"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9878000020980835,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9878000020980835,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.004600000102072954,"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.0027000000700354576,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/entropy-generation","display_name":"entropy production","score":0.9860000014305115},{"id":"https://openalex.org/keywords/boltzmann-equation","display_name":"Boltzmann equation","score":0.9259999990463257},{"id":"https://openalex.org/keywords/boltzmann-collision-operator","display_name":"Boltzmann collision operator","score":0.7929999828338623},{"id":"https://openalex.org/keywords/hard-spheres","display_name":"hard spheres","score":0.7480000257492065},{"id":"https://openalex.org/keywords/maxwell-molecules","display_name":"Maxwell molecules","score":0.9990000128746033},{"id":"https://openalex.org/keywords/non-monotonicity","display_name":"non-monotonicity","score":0.7789999842643738},{"id":"https://openalex.org/keywords/maxwellian","display_name":"Maxwellian","score":0.8199999928474426}],"concepts":[{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.6230000257492065},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6139000058174133},{"id":"https://openalex.org/C35304006","wikidata":"https://www.wikidata.org/wiki/Q5962","display_name":"Boltzmann constant","level":2,"score":0.6123999953269958},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5892000198364258},{"id":"https://openalex.org/C207282930","wikidata":"https://www.wikidata.org/wiki/Q5380811","display_name":"Entropy production","level":2,"score":0.5758000016212463},{"id":"https://openalex.org/C135889238","wikidata":"https://www.wikidata.org/wiki/Q46276","display_name":"Kinetic energy","level":2,"score":0.5351999998092651},{"id":"https://openalex.org/C121704057","wikidata":"https://www.wikidata.org/wiki/Q352070","display_name":"Collision","level":2,"score":0.531499981880188},{"id":"https://openalex.org/C33932047","wikidata":"https://www.wikidata.org/wiki/Q375553","display_name":"Boltzmann's entropy formula","level":3,"score":0.5260000228881836},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4921000003814697},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4839000105857849},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4742000102996826},{"id":"https://openalex.org/C99987037","wikidata":"https://www.wikidata.org/wiki/Q2435125","display_name":"Hard spheres","level":2,"score":0.4708000123500824},{"id":"https://openalex.org/C165995430","wikidata":"https://www.wikidata.org/wiki/Q891653","display_name":"Boltzmann equation","level":2,"score":0.43549999594688416},{"id":"https://openalex.org/C179434709","wikidata":"https://www.wikidata.org/wiki/Q899853","display_name":"H-theorem","level":5,"score":0.42910000681877136},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3912000060081482},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.3813000023365021},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.37689998745918274},{"id":"https://openalex.org/C19979193","wikidata":"https://www.wikidata.org/wiki/Q25100325","display_name":"Kinetic theory","level":2,"score":0.36469998955726624},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34279999136924744},{"id":"https://openalex.org/C203809815","wikidata":"https://www.wikidata.org/wiki/Q634965","display_name":"Maxwell\u2013Boltzmann distribution","level":3,"score":0.3183000087738037},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3133000135421753},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3077999949455261},{"id":"https://openalex.org/C2778348673","wikidata":"https://www.wikidata.org/wiki/Q739302","display_name":"Production (economics)","level":2,"score":0.2761000096797943},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.260699987411499}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.01753","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01753","pdf_url":"https://arxiv.org/pdf/2609.01753","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2609.01753","doi":"https://doi.org/10.48550/arxiv.2609.01753","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.01753","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.01753","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01753","pdf_url":"https://arxiv.org/pdf/2609.01753","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7207829101.pdf","grobid_xml":"https://content.openalex.org/works/W7207829101.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W4403443891","https://openalex.org/W4406032699","https://openalex.org/W4410294295","https://openalex.org/W4412115704","https://openalex.org/W4414909087","https://openalex.org/W4415348690","https://openalex.org/W4416042785","https://openalex.org/W4417410268","https://openalex.org/W6891944410","https://openalex.org/W7116895035","https://openalex.org/W7116917057","https://openalex.org/W7118853216","https://openalex.org/W7128614863","https://openalex.org/W7151415124"],"related_works":["https://openalex.org/W7151415124","https://openalex.org/W7211989707","https://openalex.org/W7118853216","https://openalex.org/W2109046718","https://openalex.org/W190102149","https://openalex.org/W2268731910","https://openalex.org/W7073639837","https://openalex.org/W1964257674","https://openalex.org/W2083936152","https://openalex.org/W2032023503"],"abstract_inverted_index":{"In":[0],"1966,":[1],"McKean":[2],"asked":[3],"whether":[4],"the":[5,9,24,28,32,43,50,57],"entropy":[6],"production":[7],"of":[8,53,60,69],"Boltzmann":[10,33],"equation":[11],"must":[12],"be":[13],"monotone":[14],"decreasing":[15],"in":[16,27],"time.":[17],"We":[18],"show":[19],"that":[20],"this":[21],"is":[22],"not":[23],"case":[25,52,59],"even":[26],"space-homogeneous":[29],"setting":[30],"for":[31],"collision":[34],"operator":[35],"with":[36],"a":[37],"constant":[38],"angular":[39],"cross":[40],"section":[41],"and":[42,56],"kinetic":[44],"parameter":[45],"$\u03b3\\in":[46],"[0,1]$.":[47],"This":[48],"recovers":[49],"classical":[51],"hard":[54],"spheres":[55],"simplest":[58],"Maxwell":[61],"molecules.":[62],"Our":[63],"examples":[64],"are":[65],"radially":[66],"symmetric":[67],"mixtures":[68],"Maxwellians.":[70]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-04T00:00:00"}