{"id":"https://openalex.org/W4309026302","doi":"https://doi.org/10.3390/e24111655","title":"Global Stability of the Curzon-Ahlborn Engine with a Working Substance That Satisfies the van der Waals Equation of State","display_name":"Global Stability of the Curzon-Ahlborn Engine with a Working Substance That Satisfies the van der Waals Equation of State","publication_year":2022,"publication_date":"2022-11-14","ids":{"openalex":"https://openalex.org/W4309026302","doi":"https://doi.org/10.3390/e24111655","pmid":"https://pubmed.ncbi.nlm.nih.gov/36421508"},"language":"en","primary_location":{"id":"doi:10.3390/e24111655","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24111655","pdf_url":"https://www.mdpi.com/1099-4300/24/11/1655/pdf?version=1668430825","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","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/24/11/1655/pdf?version=1668430825","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059210929","display_name":"Juan Carlos Pacheco-Paez","orcid":"https://orcid.org/0009-0000-6105-6938"},"institutions":[{"id":"https://openalex.org/I200362191","display_name":"Universidad Aut\u00f3noma Metropolitana","ror":"https://ror.org/02kta5139","country_code":"MX","type":"education","lineage":["https://openalex.org/I200362191"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Juan Carlos Pacheco-Paez","raw_affiliation_strings":["Basic Sciences Departament, Metropolitan Autonomus University, Campus Azcapotzalco, Av. San Pablo 180, Col. Reynosa, Mexico City CP 02200, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Basic Sciences Departament, Metropolitan Autonomus University, Campus Azcapotzalco, Av. San Pablo 180, Col. Reynosa, Mexico City CP 02200, Mexico","institution_ids":["https://openalex.org/I200362191"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065981833","display_name":"Juan Carlos Chimal-Egu\u00eda","orcid":"https://orcid.org/0000-0001-7134-0190"},"institutions":[{"id":"https://openalex.org/I59361560","display_name":"Instituto Polit\u00e9cnico Nacional","ror":"https://ror.org/059sp8j34","country_code":"MX","type":"education","lineage":["https://openalex.org/I59361560"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Juan Carlos Chimal-Egu\u00eda","raw_affiliation_strings":["Laboratorio de Simulaci\u00f3n y Modelado, Centro de Investigaci\u00f3n en Computaci\u00f3n, Instituto Polit\u00e9cnico Nacional, Av. Juan de Dios B\u00e1tiz s/n UP Zacatenco, Mexico City CP 07738, Mexico"],"raw_orcid":"https://orcid.org/0000-0001-7134-0190","affiliations":[{"raw_affiliation_string":"Laboratorio de Simulaci\u00f3n y Modelado, Centro de Investigaci\u00f3n en Computaci\u00f3n, Instituto Polit\u00e9cnico Nacional, Av. Juan de Dios B\u00e1tiz s/n UP Zacatenco, Mexico City CP 07738, Mexico","institution_ids":["https://openalex.org/I59361560"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072845826","display_name":"Ricardo T. Pa\u00e9z-Hern\u00e1ndez","orcid":"https://orcid.org/0000-0001-9401-8436"},"institutions":[{"id":"https://openalex.org/I200362191","display_name":"Universidad Aut\u00f3noma Metropolitana","ror":"https://ror.org/02kta5139","country_code":"MX","type":"education","lineage":["https://openalex.org/I200362191"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"Ricardo P\u00e1ez-Hern\u00e1ndez","raw_affiliation_strings":["\u00c1rea de F\u00edsica de Procesos Irreversibles, Basic Sciences Departament, Metropolitan Autonomus University, Campus Azcapotzalco, Av. San Pablo 180, Col. Reynosa, Mexico City CP 02200, Mexico"],"raw_orcid":"https://orcid.org/0000-0001-9401-8436","affiliations":[{"raw_affiliation_string":"\u00c1rea de F\u00edsica de Procesos Irreversibles, Basic Sciences Departament, Metropolitan Autonomus University, Campus Azcapotzalco, Av. San Pablo 180, Col. Reynosa, Mexico City CP 02200, Mexico","institution_ids":["https://openalex.org/I200362191"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023185161","display_name":"Delfino Ladino-Luna","orcid":null},"institutions":[{"id":"https://openalex.org/I200362191","display_name":"Universidad Aut\u00f3noma Metropolitana","ror":"https://ror.org/02kta5139","country_code":"MX","type":"education","lineage":["https://openalex.org/I200362191"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Delfino Ladino-Luna","raw_affiliation_strings":["\u00c1rea de F\u00edsica de Procesos Irreversibles, Basic Sciences Departament, Metropolitan Autonomus University, Campus Azcapotzalco, Av. San Pablo 180, Col. Reynosa, Mexico City CP 02200, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u00c1rea de F\u00edsica de Procesos Irreversibles, Basic Sciences Departament, Metropolitan Autonomus University, Campus Azcapotzalco, Av. San Pablo 180, Col. Reynosa, Mexico City CP 02200, Mexico","institution_ids":["https://openalex.org/I200362191"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5072845826"],"corresponding_institution_ids":["https://openalex.org/I200362191"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13425449,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"24","issue":"11","first_page":"1655","last_page":"1655"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":1.0,"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":1.0,"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/T12220","display_name":"Quantum Electrodynamics and Casimir Effect","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T10095","display_name":"Cosmology and Gravitation Theories","score":0.9860000014305115,"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/mathematics","display_name":"Mathematics","score":0.7294847369194031},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.7203871011734009},{"id":"https://openalex.org/keywords/van-der-waals-force","display_name":"van der Waals force","score":0.6042226552963257},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.5456157922744751},{"id":"https://openalex.org/keywords/ideal-gas","display_name":"Ideal gas","score":0.474540114402771},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4554176330566406},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.44678086042404175},{"id":"https://openalex.org/keywords/steady-state","display_name":"Steady state (chemistry)","score":0.42687517404556274},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4156859815120697},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.36073601245880127},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.18316331505775452},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14461749792099},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1386704444885254},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08839505910873413},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.05361691117286682},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.05316188931465149},{"id":"https://openalex.org/keywords/physical-chemistry","display_name":"Physical chemistry","score":0.05040180683135986}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7294847369194031},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.7203871011734009},{"id":"https://openalex.org/C126061179","wikidata":"https://www.wikidata.org/wiki/Q189627","display_name":"van der Waals force","level":3,"score":0.6042226552963257},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.5456157922744751},{"id":"https://openalex.org/C30342001","wikidata":"https://www.wikidata.org/wiki/Q172280","display_name":"Ideal gas","level":2,"score":0.474540114402771},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4554176330566406},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.44678086042404175},{"id":"https://openalex.org/C8171440","wikidata":"https://www.wikidata.org/wiki/Q903414","display_name":"Steady state (chemistry)","level":2,"score":0.42687517404556274},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4156859815120697},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.36073601245880127},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.18316331505775452},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14461749792099},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1386704444885254},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08839505910873413},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.05361691117286682},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.05316188931465149},{"id":"https://openalex.org/C147789679","wikidata":"https://www.wikidata.org/wiki/Q11372","display_name":"Physical chemistry","level":1,"score":0.05040180683135986},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C32909587","wikidata":"https://www.wikidata.org/wiki/Q11369","display_name":"Molecule","level":2,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e24111655","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24111655","pdf_url":"https://www.mdpi.com/1099-4300/24/11/1655/pdf?version=1668430825","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:36421508","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/36421508","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:doaj.org/article:068ee8f2c39b44bc9101f495d06e4052","is_oa":true,"landing_page_url":"https://doaj.org/article/068ee8f2c39b44bc9101f495d06e4052","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 24, Iss 11, p 1655 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/24/11/1655/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e24111655","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 24; Issue 11; Pages: 1655","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:9689644","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/9689644","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"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/e24111655","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24111655","pdf_url":"https://www.mdpi.com/1099-4300/24/11/1655/pdf?version=1668430825","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":[{"id":"https://openalex.org/F4320324217","display_name":"Comisi\u00f3n de Operaci\u00f3n y Fomento de Actividades Acad\u00e9micas, Instituto Polit\u00e9cnico Nacional","ror":"https://ror.org/059sp8j34"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4309026302.pdf","grobid_xml":"https://content.openalex.org/works/W4309026302.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W1966311626","https://openalex.org/W1977889978","https://openalex.org/W1981343618","https://openalex.org/W1984142080","https://openalex.org/W1990371504","https://openalex.org/W2004601957","https://openalex.org/W2014432698","https://openalex.org/W2027258966","https://openalex.org/W2037259168","https://openalex.org/W2045714750","https://openalex.org/W2046123900","https://openalex.org/W2058020634","https://openalex.org/W2058119674","https://openalex.org/W2062660690","https://openalex.org/W2064082915","https://openalex.org/W2064845598","https://openalex.org/W2080639085","https://openalex.org/W2084255008","https://openalex.org/W2094251456","https://openalex.org/W2096489362","https://openalex.org/W2101927262","https://openalex.org/W2295542807","https://openalex.org/W2348270390","https://openalex.org/W3087586163","https://openalex.org/W3100126054","https://openalex.org/W3113367643","https://openalex.org/W3140980567","https://openalex.org/W3158950734","https://openalex.org/W3194429906","https://openalex.org/W4280496527"],"related_works":["https://openalex.org/W2016023420","https://openalex.org/W4229082226","https://openalex.org/W2150857911","https://openalex.org/W1969178306","https://openalex.org/W4241994605","https://openalex.org/W2080303242","https://openalex.org/W2007624894","https://openalex.org/W2067605632","https://openalex.org/W2130151591","https://openalex.org/W4388250291"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,80,113],"show":[4],"an":[5],"analysis":[6],"of":[7,11,20,29,63,73,76,94,100,108,118],"the":[8,17,21,24,36,42,47,50,60,64,70,74,77,82,85,91,95,98,101,109,119],"global":[9],"stability":[10,44,99],"a":[12,54,115],"Curzon-Ahlborn":[13],"engine":[14,22,51],"considering":[15],"that":[16],"working":[18],"substance":[19],"satisfies":[23],"Van":[25],"der":[26],"Waals":[27],"equation":[28],"state,":[30],"which":[31],"is":[32],"more":[33],"general":[34],"than":[35],"ideal":[37],"gas":[38],"case.":[39],"We":[40,58,104],"use":[41],"Lyapunov":[43],"theory":[45],"for":[46],"case":[48],"where":[49],"operates":[52],"at":[53],"maximum":[55],"power":[56],"output.":[57],"analyze":[59],"steady":[61,102],"state":[62],"intermediate":[65],"temperatures":[66],"as":[67,69],"well":[68],"asymptotic":[71],"behavior":[72],"performance":[75],"engine.":[78],"Additionally,":[79],"study":[81],"relationship":[83],"between":[84],"inherent":[86],"time":[87],"delay":[88],"by":[89],"analyzing":[90],"dynamic":[92],"properties":[93],"system":[96],"and":[97,122],"state.":[103],"present":[105],"illustrative":[106],"graphs":[107],"obtained":[110,120],"results.":[111],"Finally,":[112],"include":[114],"brief":[116],"discussion":[117],"results":[121],"appropriate":[123],"conclusions.":[124]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}