{"id":"https://openalex.org/W2900230678","doi":"https://doi.org/10.3390/e20120925","title":"Geometry of Thermodynamic Processes","display_name":"Geometry of Thermodynamic Processes","publication_year":2018,"publication_date":"2018-12-04","ids":{"openalex":"https://openalex.org/W2900230678","doi":"https://doi.org/10.3390/e20120925","mag":"2900230678","pmid":"https://pubmed.ncbi.nlm.nih.gov/33266649"},"language":"en","primary_location":{"id":"doi:10.3390/e20120925","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e20120925","pdf_url":"https://www.mdpi.com/1099-4300/20/12/925/pdf?version=1543913775","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":["arxiv","crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/20/12/925/pdf?version=1543913775","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Arjan Van der Schaft","orcid":"https://orcid.org/0000-0002-2383-9234"},"institutions":[{"id":"https://openalex.org/I169381384","display_name":"University of Groningen","ror":"https://ror.org/012p63287","country_code":"NL","type":"education","lineage":["https://openalex.org/I169381384"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Arjan Van der Schaft","raw_affiliation_strings":["Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, Jan C. Willems Center for Systems and Control, University of Groningen, P.O. Box 407, 9700 AK Groningen, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, Jan C. Willems Center for Systems and Control, University of Groningen, P.O. Box 407, 9700 AK Groningen, The Netherlands","institution_ids":["https://openalex.org/I169381384"]}]},{"author_position":"last","author":{"id":null,"display_name":"Bernhard Maschke","orcid":"https://orcid.org/0000-0003-0221-2843"},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210143168","display_name":"Automation and Process Engineering Laboratory","ror":"https://ror.org/03kfjwy31","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I1294671590","https://openalex.org/I203339264","https://openalex.org/I4210095849","https://openalex.org/I4210143168","https://openalex.org/I59692284"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Bernhard Maschke","raw_affiliation_strings":["Laboratoire d\u2019automatique et de g\u00e9nie des proc\u00e9d\u00e9s (LAGEP) (UMR CNRS 5007), Universit\u00e9 Claude Bernard Lyon 1, CNRS, 69622 Villeurbanne, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire d\u2019automatique et de g\u00e9nie des proc\u00e9d\u00e9s (LAGEP) (UMR CNRS 5007), Universit\u00e9 Claude Bernard Lyon 1, CNRS, 69622 Villeurbanne, France","institution_ids":["https://openalex.org/I4210143168","https://openalex.org/I100532134","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I169381384"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":6.7406,"has_fulltext":false,"cited_by_count":60,"citation_normalized_percentile":{"value":0.97274438,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":100},"biblio":{"volume":"20","issue":"12","first_page":"925","last_page":"925"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9907000064849854,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9907000064849854,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.0012000000569969416,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.000699999975040555,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/symplectic-geometry","display_name":"Symplectic geometry","score":0.6829000115394592},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.5849999785423279},{"id":"https://openalex.org/keywords/contact-geometry","display_name":"Contact geometry","score":0.5838000178337097},{"id":"https://openalex.org/keywords/thermodynamic-system","display_name":"Thermodynamic system","score":0.5052000284194946},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.4758000075817108},{"id":"https://openalex.org/keywords/hamiltonian-mechanics","display_name":"Hamiltonian mechanics","score":0.4657000005245209},{"id":"https://openalex.org/keywords/submanifold","display_name":"Submanifold","score":0.4526999890804291},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.438400000333786},{"id":"https://openalex.org/keywords/thermodynamic-state","display_name":"Thermodynamic state","score":0.42989999055862427},{"id":"https://openalex.org/keywords/information-geometry","display_name":"Information geometry","score":0.42260000109672546}],"concepts":[{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.6829000115394592},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.5849999785423279},{"id":"https://openalex.org/C74544821","wikidata":"https://www.wikidata.org/wiki/Q1783105","display_name":"Contact geometry","level":2,"score":0.5838000178337097},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5343000292778015},{"id":"https://openalex.org/C14380042","wikidata":"https://www.wikidata.org/wiki/Q503327","display_name":"Thermodynamic system","level":2,"score":0.5052000284194946},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.4758000075817108},{"id":"https://openalex.org/C136864674","wikidata":"https://www.wikidata.org/wiki/Q477921","display_name":"Hamiltonian mechanics","level":3,"score":0.4657000005245209},{"id":"https://openalex.org/C151300846","wikidata":"https://www.wikidata.org/wiki/Q125539","display_name":"Submanifold","level":2,"score":0.4526999890804291},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.438400000333786},{"id":"https://openalex.org/C12668873","wikidata":"https://www.wikidata.org/wiki/Q230875","display_name":"Thermodynamic state","level":3,"score":0.42989999055862427},{"id":"https://openalex.org/C109546454","wikidata":"https://www.wikidata.org/wiki/Q3798604","display_name":"Information geometry","level":4,"score":0.42260000109672546},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.41280001401901245},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.40540000796318054},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.39890000224113464},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.36399999260902405},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3513999879360199},{"id":"https://openalex.org/C181104567","wikidata":"https://www.wikidata.org/wiki/Q761383","display_name":"Riemannian geometry","level":2,"score":0.34040001034736633},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.335999995470047},{"id":"https://openalex.org/C39920418","wikidata":"https://www.wikidata.org/wiki/Q11476","display_name":"Kinematics","level":2,"score":0.32739999890327454},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.3269999921321869},{"id":"https://openalex.org/C105236789","wikidata":"https://www.wikidata.org/wiki/Q213016","display_name":"Thermodynamic process","level":3,"score":0.32429999113082886},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.3206999897956848},{"id":"https://openalex.org/C206444204","wikidata":"https://www.wikidata.org/wiki/Q17086162","display_name":"Geometric mechanics","level":5,"score":0.31459999084472656},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3140999972820282},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.3100000023841858},{"id":"https://openalex.org/C106402246","wikidata":"https://www.wikidata.org/wiki/Q528525","display_name":"Homogeneous coordinates","level":2,"score":0.3082999885082245},{"id":"https://openalex.org/C94906876","wikidata":"https://www.wikidata.org/wiki/Q1132952","display_name":"Homogeneous function","level":3,"score":0.296099990606308},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.29170000553131104},{"id":"https://openalex.org/C110202963","wikidata":"https://www.wikidata.org/wiki/Q1783542","display_name":"Convex geometry","level":5,"score":0.27730000019073486},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.27730000019073486},{"id":"https://openalex.org/C152401794","wikidata":"https://www.wikidata.org/wiki/Q583760","display_name":"Antisymmetric relation","level":2,"score":0.274399995803833},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.27309998869895935},{"id":"https://openalex.org/C41607394","wikidata":"https://www.wikidata.org/wiki/Q2420179","display_name":"Thermodynamic potential","level":2,"score":0.2667999863624573},{"id":"https://openalex.org/C131157278","wikidata":"https://www.wikidata.org/wiki/Q51363","display_name":"Thermodynamic equilibrium","level":2,"score":0.2635999917984009},{"id":"https://openalex.org/C207282930","wikidata":"https://www.wikidata.org/wiki/Q5380811","display_name":"Entropy production","level":2,"score":0.2583000063896179},{"id":"https://openalex.org/C154968394","wikidata":"https://www.wikidata.org/wiki/Q5535474","display_name":"Geometric analysis","level":5,"score":0.2551000118255615},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.25429999828338623},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.2506999969482422}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.3390/e20120925","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e20120925","pdf_url":"https://www.mdpi.com/1099-4300/20/12/925/pdf?version=1543913775","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:33266649","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33266649","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:arXiv.org:1811.04227","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1811.04227","pdf_url":"https://arxiv.org/pdf/1811.04227","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"pmh:oai:pure.rug.nl:publications/da83ac68-53f6-4166-9a42-3a61e802073b","is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/da83ac68-53f6-4166-9a42-3a61e802073b","pdf_url":"https://pure.rug.nl/ws/files/76314074/entropy_20_00925.pdf","source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"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":"van der Schaft, A & Maschke, B 2018, 'Geometry of Thermodynamic Processes', Entropy, vol. 20, no. 12, 925. https://doi.org/10.3390/e20120925","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:doaj.org/article:966c3636480847129f3d3214576d23ee","is_oa":true,"landing_page_url":"https://doaj.org/article/966c3636480847129f3d3214576d23ee","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 20, Iss 12, p 925 (2018)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/20/12/925/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e20120925","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:7512512","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7512512","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","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":"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"}],"best_oa_location":{"id":"doi:10.3390/e20120925","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e20120925","pdf_url":"https://www.mdpi.com/1099-4300/20/12/925/pdf?version=1543913775","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/W2900230678.pdf","grobid_xml":"https://content.openalex.org/works/W2900230678.grobid-xml"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W1503283896","https://openalex.org/W1553823556","https://openalex.org/W1578706793","https://openalex.org/W1928035255","https://openalex.org/W1964373008","https://openalex.org/W1966271976","https://openalex.org/W1974571176","https://openalex.org/W1983696948","https://openalex.org/W2018152530","https://openalex.org/W2024177714","https://openalex.org/W2028710371","https://openalex.org/W2044492748","https://openalex.org/W2057455674","https://openalex.org/W2059206957","https://openalex.org/W2064854048","https://openalex.org/W2071140831","https://openalex.org/W2071449583","https://openalex.org/W2075878724","https://openalex.org/W2077085908","https://openalex.org/W2085058149","https://openalex.org/W2087793319","https://openalex.org/W2089121607","https://openalex.org/W2093827309","https://openalex.org/W2095477585","https://openalex.org/W2096876511","https://openalex.org/W2126479355","https://openalex.org/W2127665720","https://openalex.org/W2141445256","https://openalex.org/W2144355672","https://openalex.org/W2144939122","https://openalex.org/W2403920481","https://openalex.org/W2485135680","https://openalex.org/W2530863578","https://openalex.org/W2555254196","https://openalex.org/W2765911775","https://openalex.org/W2796618235","https://openalex.org/W2808859382","https://openalex.org/W2809648346","https://openalex.org/W4292402580","https://openalex.org/W4299992430"],"related_works":[],"abstract_inverted_index":{"Since":[0],"the":[1,13,32,50,60,67,77,82,88,121,127,148,154],"1970s,":[2],"contact":[3,35,136],"geometry":[4,137],"has":[5,28],"been":[6,29],"recognized":[7],"as":[8],"an":[9],"appropriate":[10],"framework":[11,162],"for":[12,175],"geometric":[14,69,97,161],"formulation":[15,98,155],"of":[16,34,55,71,91,101,107,117,150,156,168],"thermodynamic":[17,57,103],"systems,":[18],"and":[19,52,93,124,138,153,177],"in":[20,105,120,135,142],"particular":[21],"their":[22,139],"state":[23,83],"properties.":[24],"More":[25],"recently":[26],"it":[27],"shown":[30],"how":[31],"symplectization":[33],"manifolds":[36],"provides":[37],"a":[38,56,72,96,166],"new":[39],"vantage":[40],"point;":[41],"enabling,":[42],"among":[43],"other":[44],"things,":[45],"to":[46,147],"switch":[47],"easily":[48],"between":[49,133],"energy":[51],"entropy":[53],"representations":[54],"system.":[58],"In":[59],"present":[61],"paper,":[62],"this":[63],"is":[64,86,99,145,163],"continued":[65],"towards":[66],"global":[68],"definition":[70,149],"degenerate":[73],"Riemannian":[74],"metric":[75],"on":[76,126,165],"homogeneous":[78,116,128,140],"Lagrangian":[79,129],"submanifold":[80],"describing":[81],"properties,":[84],"which":[85],"overarching":[87],"locally-defined":[89],"metrics":[90],"Weinhold":[92],"Ruppeiner.":[94],"Next,":[95],"given":[100],"non-equilibrium":[102],"processes,":[104],"terms":[106],"Hamiltonian":[108,112],"dynamics":[109],"defined":[110],"by":[111],"functions":[113],"that":[114],"are":[115],"degree":[118],"one":[119],"co-extensive":[122],"variables":[123],"zero":[125],"submanifold.":[130],"The":[131,159],"correspondence":[132],"objects":[134],"counterparts":[141],"symplectic":[143],"geometry,":[144],"extended":[146],"port-thermodynamic":[151],"systems":[152],"interconnection":[157],"ports.":[158],"resulting":[160],"illustrated":[164],"number":[167],"simple":[169],"examples,":[170],"already":[171],"indicating":[172],"its":[173],"potential":[174],"analysis":[176],"control.":[178]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":16},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":10}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2018-11-16T00:00:00"}
