{"id":"https://openalex.org/W7213502603","doi":"https://doi.org/10.48550/arxiv.2609.18215","title":"Maxwell's relations as Hamilton's equations: a symplectic and variational framework","display_name":"Maxwell's relations as Hamilton's equations: a symplectic and variational framework","publication_year":2026,"publication_date":"2026-09-16","ids":{"openalex":"https://openalex.org/W7213502603","doi":"https://doi.org/10.48550/arxiv.2609.18215"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.18215","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18215","pdf_url":"https://arxiv.org/pdf/2609.18215","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/2609.18215","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076151732","display_name":"Sikarin Yoo-Kong","orcid":"https://orcid.org/0000-0002-6604-8686","observed_orcids":["https://orcid.org/0000-0002-6604-8686"]},"institutions":[{"id":"https://openalex.org/I66200439","display_name":"Naresuan University","ror":"https://ror.org/03e2qe334","country_code":"TH","type":"education","lineage":["https://openalex.org/I66200439"]}],"countries":["TH"],"is_corresponding":true,"raw_author_name":"Yoo-Kong, Sikarin","raw_affiliation_strings":["The Institute for Fundamental Study (IF) , Naresuan University , Phitsanulok , Thailand , 65000"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Institute for Fundamental Study (IF) , Naresuan University , Phitsanulok , Thailand , 65000","institution_ids":["https://openalex.org/I66200439"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5076151732"],"corresponding_institution_ids":["https://openalex.org/I66200439"],"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.8529999852180481,"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":0.8529999852180481,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.056299999356269836,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11960","display_name":"Relativity and Gravitational Theory","score":0.027499999850988388,"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/maxwell-s-relations","display_name":"Maxwell's relations","score":0.968999981880188},{"id":"https://openalex.org/keywords/hamilton-s-equations","display_name":"Hamilton's equations","score":0.925000011920929},{"id":"https://openalex.org/keywords/classical-thermodynamics","display_name":"classical thermodynamics","score":0.8579999804496765},{"id":"https://openalex.org/keywords/hamiltonian-systems","display_name":"Hamiltonian systems","score":0.8370000123977661},{"id":"https://openalex.org/keywords/thermodynamic-potential","display_name":"thermodynamic potential","score":0.7409999966621399},{"id":"https://openalex.org/keywords/variational-principle","display_name":"variational principle","score":0.6899999976158142},{"id":"https://openalex.org/keywords/conserved-quantities","display_name":"first integrals","score":0.8619999885559082},{"id":"https://openalex.org/keywords/adiabatic-processes","display_name":"adiabatic processes","score":0.9760000109672546},{"id":"https://openalex.org/keywords/ideal-gas","display_name":"ideal gas","score":0.9020000100135803},{"id":"https://openalex.org/keywords/symplectic-geometry","display_name":"symplectic geometry","score":0.8410000205039978}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7145000100135803},{"id":"https://openalex.org/C113174994","wikidata":"https://www.wikidata.org/wiki/Q4120602","display_name":"Thermodynamic equations","level":3,"score":0.5426999926567078},{"id":"https://openalex.org/C109663097","wikidata":"https://www.wikidata.org/wiki/Q182453","display_name":"Adiabatic process","level":2,"score":0.5361999869346619},{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.5357000231742859},{"id":"https://openalex.org/C14380042","wikidata":"https://www.wikidata.org/wiki/Q503327","display_name":"Thermodynamic system","level":2,"score":0.4934000074863434},{"id":"https://openalex.org/C12668873","wikidata":"https://www.wikidata.org/wiki/Q230875","display_name":"Thermodynamic state","level":3,"score":0.46389999985694885},{"id":"https://openalex.org/C9259290","wikidata":"https://www.wikidata.org/wiki/Q745215","display_name":"Variational principle","level":2,"score":0.4431000053882599},{"id":"https://openalex.org/C136864674","wikidata":"https://www.wikidata.org/wiki/Q477921","display_name":"Hamiltonian mechanics","level":3,"score":0.4431000053882599},{"id":"https://openalex.org/C143218062","wikidata":"https://www.wikidata.org/wiki/Q722799","display_name":"Principle of least action","level":2,"score":0.42239999771118164},{"id":"https://openalex.org/C30342001","wikidata":"https://www.wikidata.org/wiki/Q172280","display_name":"Ideal gas","level":2,"score":0.4207000136375427},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.4099000096321106},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4090999960899353},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.40639999508857727},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.3853999972343445},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.38510000705718994},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.37139999866485596},{"id":"https://openalex.org/C131157278","wikidata":"https://www.wikidata.org/wiki/Q51363","display_name":"Thermodynamic equilibrium","level":2,"score":0.36660000681877136},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.3637000024318695},{"id":"https://openalex.org/C3379466","wikidata":"https://www.wikidata.org/wiki/Q1501876","display_name":"Canonical coordinates","level":3,"score":0.3634999990463257},{"id":"https://openalex.org/C105236789","wikidata":"https://www.wikidata.org/wiki/Q213016","display_name":"Thermodynamic process","level":3,"score":0.3463999927043915},{"id":"https://openalex.org/C71914180","wikidata":"https://www.wikidata.org/wiki/Q1071013","display_name":"Conserved quantity","level":2,"score":0.33959999680519104},{"id":"https://openalex.org/C52154503","wikidata":"https://www.wikidata.org/wiki/Q7915797","display_name":"Variational integrator","level":4,"score":0.3278000056743622},{"id":"https://openalex.org/C28062496","wikidata":"https://www.wikidata.org/wiki/Q1145653","display_name":"Hamilton's principle","level":3,"score":0.3262999951839447},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.3239000141620636},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.31360000371932983},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.313400000333786},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.31200000643730164},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.3093000054359436},{"id":"https://openalex.org/C93812963","wikidata":"https://www.wikidata.org/wiki/Q7249433","display_name":"Projected dynamical system","level":5,"score":0.30799999833106995},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30410000681877136},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.2953000068664551},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.2816999852657318},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.28110000491142273},{"id":"https://openalex.org/C97491812","wikidata":"https://www.wikidata.org/wiki/Q6060414","display_name":"Inverse problem for Lagrangian mechanics","level":4,"score":0.2540999948978424}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.18215","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18215","pdf_url":"https://arxiv.org/pdf/2609.18215","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.2609.18215","doi":"https://doi.org/10.48550/arxiv.2609.18215","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.18215","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.18215","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.18215","pdf_url":"https://arxiv.org/pdf/2609.18215","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/F4320323020","display_name":"Naresuan University","ror":"https://ror.org/03e2qe334"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213502603.pdf","grobid_xml":"https://content.openalex.org/works/W7213502603.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2095416251","https://openalex.org/W3000208598","https://openalex.org/W1974107863","https://openalex.org/W2053089053","https://openalex.org/W2058503569","https://openalex.org/W3108740625","https://openalex.org/W4206322007","https://openalex.org/W2339769315","https://openalex.org/W7097286698","https://openalex.org/W7096640696"],"abstract_inverted_index":{"We":[0],"develop":[1],"a":[2,12,47,86,94,119],"geometric":[3,120],"framework":[4],"in":[5,33,68],"which":[6],"classical":[7],"thermodynamics":[8],"is":[9,118],"reformulated":[10],"as":[11,24,44,61],"Hamiltonian":[13],"dynamical":[14],"system.":[15],"An":[16],"explicit":[17,74],"canonical":[18],"mapping":[19],"$(q,p,t,H)\\leftrightarrow(V,-P,S,-T)$":[20],"identifies":[21],"Maxwell's":[22],"relations":[23,54],"the":[25,29,52,56,90,102,108],"characteristic":[26],"equations":[27,38,78],"of":[28,39,114,122],"thermodynamic":[30,42,57,115],"Poincar\u00e9--Cartan":[31],"one-form,":[32],"direct":[34],"parallel":[35],"with":[36],"Hamilton's":[37],"motion.":[40],"Treating":[41],"potentials":[43],"action":[45],"functionals,":[46],"variational":[48],"principle":[49],"recovers":[50],"both":[51],"Maxwell":[53],"and":[55,81],"constraints":[58],"(adiabaticity,":[59],"isothermality)":[60],"conserved":[62],"first":[63],"integrals.":[64],"For":[65],"adiabatic":[66],"processes":[67],"an":[69,127],"ideal":[70],"gas,":[71],"this":[72],"yields":[73],"second-order":[75],"ordinary":[76],"differential":[77],"for":[79],"$V(T)$":[80],"$P(T)$,":[82],"each":[83],"governed":[84],"by":[85],"temperature-dependent":[87],"Lagrangian.":[88],"Assembling":[89],"component":[91],"Lagrangians":[92],"into":[93],"multi-parameter":[95],"Lagrangian":[96],"1-form":[97],"$\\mathcal{L}$,":[98],"we":[99],"prove":[100],"that":[101,112],"closure":[103],"condition":[104],"$d\\mathcal{L}=0$":[105],"holds":[106],"on":[107],"solution":[109],"manifold,":[110],"establishing":[111],"path-independence":[113],"state":[116],"functions":[117],"consequence":[121],"multi-time":[123],"integrability":[124],"rather":[125],"than":[126],"independent":[128],"postulate.":[129]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-18T00:00:00"}
