{"id":"https://openalex.org/W2099613501","doi":"https://doi.org/10.3390/e14020092","title":"The Rate-Controlled Constrained-Equilibrium Approach to Far-From-Local-Equilibrium Thermodynamics","display_name":"The Rate-Controlled Constrained-Equilibrium Approach to Far-From-Local-Equilibrium Thermodynamics","publication_year":2012,"publication_date":"2012-01-30","ids":{"openalex":"https://openalex.org/W2099613501","doi":"https://doi.org/10.3390/e14020092","mag":"2099613501"},"language":"en","primary_location":{"id":"doi:10.3390/e14020092","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e14020092","pdf_url":"https://www.mdpi.com/1099-4300/14/2/92/pdf?version=1424784843","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/1099-4300/14/2/92/pdf?version=1424784843","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039539766","display_name":"Gian Paolo Beretta","orcid":"https://orcid.org/0000-0001-9302-2468"},"institutions":[{"id":"https://openalex.org/I79940851","display_name":"University of Brescia","ror":"https://ror.org/02q2d2610","country_code":"IT","type":"education","lineage":["https://openalex.org/I79940851"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Gian Paolo Beretta","raw_affiliation_strings":["Department of Mechanical and Industrial Engineering, Universita di Brescia, Brescia, 25123, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Industrial Engineering, Universita di Brescia, Brescia, 25123, Italy","institution_ids":["https://openalex.org/I79940851"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050391951","display_name":"James C. Keck","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"James C. Keck","raw_affiliation_strings":["Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034333231","display_name":"Mohammad Janbozorgi","orcid":null},"institutions":[{"id":"https://openalex.org/I12912129","display_name":"Northeastern University","ror":"https://ror.org/04t5xt781","country_code":"US","type":"education","lineage":["https://openalex.org/I12912129"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mohammad Janbozorgi","raw_affiliation_strings":["Department of Mechanical Engineering, Northeastern University Boston, MA 02115, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Northeastern University Boston, MA 02115, USA","institution_ids":["https://openalex.org/I12912129"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019119734","display_name":"Hameed Metghalchi","orcid":null},"institutions":[{"id":"https://openalex.org/I12912129","display_name":"Northeastern University","ror":"https://ror.org/04t5xt781","country_code":"US","type":"education","lineage":["https://openalex.org/I12912129"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hameed Metghalchi","raw_affiliation_strings":["Department of Mechanical Engineering, Northeastern University Boston, MA 02115, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Northeastern University Boston, MA 02115, USA","institution_ids":["https://openalex.org/I12912129"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5039539766"],"corresponding_institution_ids":["https://openalex.org/I79940851"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":5.5979,"has_fulltext":true,"cited_by_count":52,"citation_normalized_percentile":{"value":0.96258459,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"14","issue":"2","first_page":"92","last_page":"130"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10553","display_name":"Combustion and flame dynamics","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10553","display_name":"Combustion and flame dynamics","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9961000084877014,"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/T10117","display_name":"Advanced Combustion Engine Technologies","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/1507","display_name":"Fluid Flow and Transfer Processes"},"field":{"id":"https://openalex.org/fields/15","display_name":"Chemical Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.6176772713661194},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5491290092468262},{"id":"https://openalex.org/keywords/equilibrium-thermodynamics","display_name":"Equilibrium thermodynamics","score":0.5058341026306152},{"id":"https://openalex.org/keywords/thermodynamic-equilibrium","display_name":"Thermodynamic equilibrium","score":0.4661494493484497},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44958826899528503},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.4379408657550812},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.4264867305755615},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3720690608024597},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3389242887496948},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23832297325134277}],"concepts":[{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.6176772713661194},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5491290092468262},{"id":"https://openalex.org/C111663737","wikidata":"https://www.wikidata.org/wiki/Q10860570","display_name":"Equilibrium thermodynamics","level":3,"score":0.5058341026306152},{"id":"https://openalex.org/C131157278","wikidata":"https://www.wikidata.org/wiki/Q51363","display_name":"Thermodynamic equilibrium","level":2,"score":0.4661494493484497},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44958826899528503},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.4379408657550812},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.4264867305755615},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3720690608024597},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3389242887496948},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23832297325134277},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e14020092","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e14020092","pdf_url":"https://www.mdpi.com/1099-4300/14/2/92/pdf?version=1424784843","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:doaj.org/article:398d2c0f0bd544b68d41c39fb2d8a8ac","is_oa":true,"landing_page_url":"https://doaj.org/article/398d2c0f0bd544b68d41c39fb2d8a8ac","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"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 14, Iss 2, Pp 92-130 (2012)","raw_type":"article"},{"id":"pmh:oai:iris.unibs.it:11379/123913","is_oa":true,"landing_page_url":"http://hdl.handle.net/11379/123913","pdf_url":null,"source":{"id":"https://openalex.org/S4306400804","display_name":"Institutional Research Information System (Universit\u00e0 degli Studi di Brescia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66752286","host_organization_name":"University of Milano-Bicocca","host_organization_lineage":["https://openalex.org/I66752286"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:mdpi.com:/1099-4300/14/2/92/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e14020092","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 14; Issue 2; Pages: 92-130","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e14020092","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e14020092","pdf_url":"https://www.mdpi.com/1099-4300/14/2/92/pdf?version=1424784843","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":[{"id":"https://openalex.org/G3622582212","display_name":null,"funder_award_id":"W911NF-08-1","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G7210208826","display_name":null,"funder_award_id":"2008-2290","funder_id":"https://openalex.org/F4320321499","funder_display_name":"Fondazione Cariplo"},{"id":"https://openalex.org/G7452299184","display_name":null,"funder_award_id":"W911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"id":"https://openalex.org/F4320321499","display_name":"Fondazione Cariplo","ror":"https://ror.org/01gb56c55"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2099613501.pdf","grobid_xml":"https://content.openalex.org/works/W2099613501.grobid-xml"},"referenced_works_count":77,"referenced_works":["https://openalex.org/W195643480","https://openalex.org/W1597618836","https://openalex.org/W1764256057","https://openalex.org/W1942193318","https://openalex.org/W1963717000","https://openalex.org/W1964373736","https://openalex.org/W1964997395","https://openalex.org/W1966113499","https://openalex.org/W1967242950","https://openalex.org/W1968003814","https://openalex.org/W1969670130","https://openalex.org/W1973890190","https://openalex.org/W1976711793","https://openalex.org/W1978122290","https://openalex.org/W1980424805","https://openalex.org/W1983874169","https://openalex.org/W1985205248","https://openalex.org/W1986736641","https://openalex.org/W1991495523","https://openalex.org/W1995875735","https://openalex.org/W1996405985","https://openalex.org/W1997586090","https://openalex.org/W2002703161","https://openalex.org/W2018670096","https://openalex.org/W2019768978","https://openalex.org/W2024056314","https://openalex.org/W2026427707","https://openalex.org/W2027892556","https://openalex.org/W2028160872","https://openalex.org/W2034091978","https://openalex.org/W2035502912","https://openalex.org/W2038239929","https://openalex.org/W2038919717","https://openalex.org/W2039906103","https://openalex.org/W2041837206","https://openalex.org/W2046744518","https://openalex.org/W2048774470","https://openalex.org/W2049967797","https://openalex.org/W2051955770","https://openalex.org/W2052720729","https://openalex.org/W2052832898","https://openalex.org/W2053744670","https://openalex.org/W2054730148","https://openalex.org/W2054914927","https://openalex.org/W2054983146","https://openalex.org/W2056033381","https://openalex.org/W2056892346","https://openalex.org/W2059650134","https://openalex.org/W2064277607","https://openalex.org/W2065615465","https://openalex.org/W2068902190","https://openalex.org/W2072480667","https://openalex.org/W2074401358","https://openalex.org/W2075047659","https://openalex.org/W2076409035","https://openalex.org/W2081339765","https://openalex.org/W2088989631","https://openalex.org/W2093568659","https://openalex.org/W2098711726","https://openalex.org/W2100939440","https://openalex.org/W2120111799","https://openalex.org/W2123088883","https://openalex.org/W2131867720","https://openalex.org/W2132597334","https://openalex.org/W2137873244","https://openalex.org/W2138278836","https://openalex.org/W2141906015","https://openalex.org/W2149219675","https://openalex.org/W2150476133","https://openalex.org/W2263958071","https://openalex.org/W3104384660","https://openalex.org/W4252065447","https://openalex.org/W4299551239","https://openalex.org/W6637735139","https://openalex.org/W6640530592","https://openalex.org/W6675400555","https://openalex.org/W6693264812"],"related_works":["https://openalex.org/W78286867","https://openalex.org/W2028369878","https://openalex.org/W1987960463","https://openalex.org/W2951854050","https://openalex.org/W4285211793","https://openalex.org/W2040098199","https://openalex.org/W4249206313","https://openalex.org/W4298067649","https://openalex.org/W196387368","https://openalex.org/W3142620627"],"abstract_inverted_index":{"The":[0,71],"Rate-Controlled":[1],"Constrained-Equilibrium":[2],"(RCCE)":[3],"method":[4,24,83,107],"for":[5,25,114],"the":[6,9,34,59,67,79,82,85,93,103,106,122,147,150,162,165,168,174,178,192,196],"description":[7],"of":[8,12,36,61,74,81,89,105,146,153,156,167,177,185,195],"time-dependent":[10],"behavior":[11],"dynamical":[13],"systems":[14,56],"in":[15,33,53,92,108,121],"non-equilibrium":[16],"states":[17],"is":[18,45],"a":[19,62,109],"general,":[20],"effective,":[21],"physically":[22],"based":[23],"model":[26],"order":[27],"reduction":[28],"that":[29,48],"was":[30],"originally":[31],"developed":[32],"framework":[35],"thermodynamics":[37],"and":[38,84,130,141,173],"chemical":[39,94,124,154],"kinetics.":[40],"A":[41],"generalized":[42,72,110],"mathematical":[43],"formulation":[44,73],"presented":[46],"here":[47],"allows":[49],"including":[50],"nonlinear":[51],"constraints":[52],"non-local":[54],"equilibrium":[55],"characterized":[57],"by":[58],"existence":[60],"non-increasing":[63],"Lyapunov":[64],"functional":[65,134],"under":[66],"system\u2019s":[68],"internal":[69],"dynamics.":[70],"RCCE":[75,186,197],"enables":[76],"to":[77,138,190],"clarify":[78,142],"essentials":[80],"built-in":[86],"general":[87],"feature":[88],"thermodynamic":[90,175],"consistency":[91,176],"kinetics":[95,125,155],"context.":[96],"In":[97,149],"this":[98],"paper,":[99],"we":[100,116,160],"work":[101],"out":[102,132,140],"details":[104],"mathematical-physics":[111],"framework,":[112],"but":[113],"definiteness":[115],"detail":[117,128],"its":[118],"well-known":[119],"implementation":[120],"traditional":[123],"framework.":[126],"We":[127,180],"proofs":[129],"spell":[131],"explicit":[133],"dependences":[135],"so":[136],"as":[137],"bring":[139],"each":[143],"underlying":[144],"assumption":[145],"method.":[148,179,198],"standard":[151],"context":[152],"ideal":[157],"gas":[158],"mixtures,":[159],"discuss":[161,182],"relations":[163],"between":[164],"validity":[166],"detailed":[169],"balance":[170],"condition":[171],"off-equilibrium":[172],"also":[181],"two":[183],"examples":[184],"gas-phase":[187],"combustion":[188],"calculations":[189],"emphasize":[191],"constraint-dependent":[193],"performance":[194]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
