{"id":"https://openalex.org/W7220383485","doi":"https://doi.org/10.48550/arxiv.2610.03060","title":"The monatomic limit of polyatomic gases as concentration of the internal-energy measure","display_name":"The monatomic limit of polyatomic gases as concentration of the internal-energy measure","publication_year":2026,"publication_date":"2026-10-02","ids":{"openalex":"https://openalex.org/W7220383485","doi":"https://doi.org/10.48550/arxiv.2610.03060"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.03060","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03060","pdf_url":"https://arxiv.org/pdf/2610.03060","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/2610.03060","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030841694","display_name":"Tommaso Ruggeri","orcid":"https://orcid.org/0000-0002-7588-2074","observed_orcids":["https://orcid.org/0000-0002-7588-2074"]},"institutions":[{"id":"https://openalex.org/I2801187332","display_name":"Accademia Nazionale dei Lincei","ror":"https://ror.org/05wfehw39","country_code":"IT","type":"other","lineage":["https://openalex.org/I2801187332"]},{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Ruggeri, Tommaso","raw_affiliation_strings":["Accademia Nazionale dei Lincei , Rome , Italy","Department of Mathematics , University of Bologna , Bologna , Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Accademia Nazionale dei Lincei , Rome , Italy","institution_ids":["https://openalex.org/I2801187332"]},{"raw_affiliation_string":"Department of Mathematics , University of Bologna , Bologna , Italy","institution_ids":["https://openalex.org/I9360294"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5030841694"],"corresponding_institution_ids":["https://openalex.org/I2801187332","https://openalex.org/I9360294"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"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":0.9984999895095825,"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":0.9984999895095825,"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":0.0005000000237487257,"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":9.999999747378752e-05,"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/polyatomic-gases","display_name":"polyatomic gases","score":0.9940000176429749},{"id":"https://openalex.org/keywords/internal-energy-distribution","display_name":"internal energy distribution","score":0.6579999923706055},{"id":"https://openalex.org/keywords/dirac-delta-function","display_name":"Dirac delta function","score":0.49300000071525574},{"id":"https://openalex.org/keywords/rational-extended-thermodynamics","display_name":"rational extended thermodynamics","score":0.7009999752044678},{"id":"https://openalex.org/keywords/gamma-distribution","display_name":"gamma distribution","score":0.7080000042915344},{"id":"https://openalex.org/keywords/relativistic-thermodynamics","display_name":"relativistic thermodynamics","score":0.6850000023841858},{"id":"https://openalex.org/keywords/constitutive-model","display_name":"constitutive equations","score":0.47999998927116394},{"id":"https://openalex.org/keywords/energy-identity","display_name":"energy identity","score":0.6510000228881836}],"concepts":[{"id":"https://openalex.org/C152149077","wikidata":"https://www.wikidata.org/wiki/Q1588896","display_name":"Monatomic ion","level":2,"score":0.8959000110626221},{"id":"https://openalex.org/C46844702","wikidata":"https://www.wikidata.org/wiki/Q2656117","display_name":"Monatomic gas","level":2,"score":0.8176000118255615},{"id":"https://openalex.org/C66594872","wikidata":"https://www.wikidata.org/wiki/Q1064242","display_name":"Polyatomic ion","level":3,"score":0.7651000022888184},{"id":"https://openalex.org/C65494353","wikidata":"https://www.wikidata.org/wiki/Q180241","display_name":"Internal energy","level":2,"score":0.6575000286102295},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5411999821662903},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5085999965667725},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4934999942779541},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4745999872684479},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3896999955177307},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3303000032901764},{"id":"https://openalex.org/C30342001","wikidata":"https://www.wikidata.org/wiki/Q172280","display_name":"Ideal gas","level":2,"score":0.3269999921321869},{"id":"https://openalex.org/C84551667","wikidata":"https://www.wikidata.org/wiki/Q155640","display_name":"Potential energy","level":2,"score":0.3165000081062317},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.30660000443458557},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.30489999055862427},{"id":"https://openalex.org/C186603090","wikidata":"https://www.wikidata.org/wiki/Q55505926","display_name":"Distribution function","level":2,"score":0.2955999970436096},{"id":"https://openalex.org/C131157278","wikidata":"https://www.wikidata.org/wiki/Q51363","display_name":"Thermodynamic equilibrium","level":2,"score":0.27730000019073486},{"id":"https://openalex.org/C61039578","wikidata":"https://www.wikidata.org/wiki/Q604279","display_name":"Dirac (video compression format)","level":3,"score":0.2766000032424927},{"id":"https://openalex.org/C97278139","wikidata":"https://www.wikidata.org/wiki/Q81182","display_name":"Absolute zero","level":2,"score":0.27250000834465027},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.2718000113964081},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.2667999863624573},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.25929999351501465},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.2522999942302704},{"id":"https://openalex.org/C99874945","wikidata":"https://www.wikidata.org/wiki/Q188715","display_name":"Statistical mechanics","level":2,"score":0.25220000743865967}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.03060","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03060","pdf_url":"https://arxiv.org/pdf/2610.03060","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.2610.03060","doi":"https://doi.org/10.48550/arxiv.2610.03060","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.03060","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:2610.03060","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03060","pdf_url":"https://arxiv.org/pdf/2610.03060","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":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320334080","display_name":"Gruppo Nazionale per la Fisica Matematica","ror":"https://ror.org/01d6bq278"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220383485.pdf","grobid_xml":"https://content.openalex.org/works/W7220383485.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4389850769","https://openalex.org/W2811394779","https://openalex.org/W3170021009","https://openalex.org/W2400518170","https://openalex.org/W2560231926","https://openalex.org/W3171959303","https://openalex.org/W2790868783","https://openalex.org/W2342130894","https://openalex.org/W1995377381","https://openalex.org/W3129038588"],"abstract_inverted_index":{"In":[0,50,102],"Rational":[1],"Extended":[2],"Thermodynamics,":[3],"the":[4,14,23,28,43,53,65,86,90,96,103,106,116,129,133],"monatomic":[5,87],"limit":[6],"of":[7,27,42],"polyatomic":[8],"gases":[9],"is":[10,109],"often":[11],"singular.":[12],"For":[13],"internal-state":[15],"density":[16],"$\u03d5(I)=I^a$,":[17],"with":[18,89],"$a=(D-5)/2$,":[19],"we":[20,122],"prove":[21],"that":[22],"normalized":[24],"equilibrium":[25,58],"distribution":[26],"molecular":[29],"internal":[30,107],"energy":[31,55,108,126],"$I$":[32],"concentrates":[33],"at":[34,72,113],"$I=0$":[35],"as":[36],"$D\\to3$,":[37],"providing":[38],"a":[39,69],"rigorous":[40],"justification":[41],"Dirac":[44],"prescription":[45],"and":[46,121,128],"its":[47],"first-order":[48],"correction.":[49],"classical":[51],"ET14,":[52],"internal-mode":[54],"differs":[56],"from":[57],"by":[59],"$-3\u03a0/2$;":[60],"positivity":[61],"yields":[62],"$-p<\u03a0<(D-3)p/3$,":[63],"while":[64],"exact":[66,125],"entropy":[67],"develops":[68],"boundary":[70],"corner":[71],"$\u03a0=0$.":[73],"Negative":[74],"dynamic":[75],"pressures":[76],"remain":[77],"admissible,":[78],"but":[79],"fixed":[80,114],"negative":[81],"values":[82],"do":[83],"not":[84],"approach":[85],"state":[88],"prescribed":[91],"total":[92],"energy.":[93,135],"This":[94],"explains":[95],"need":[97],"for":[98],"compatible":[99],"initial":[100],"data.":[101],"relativistic":[104],"case,":[105],"conditionally":[110],"gamma":[111],"distributed":[112],"momentum;":[115],"constitutive":[117],"integrals":[118],"follow":[119],"directly,":[120],"derive":[123],"an":[124],"identity":[127],"first":[130],"correction":[131],"to":[132],"Synge":[134]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-06T00:00:00"}
