{"id":"https://openalex.org/W1988508167","doi":"https://doi.org/10.3390/e14030407","title":"Temporal Asymmetry, Entropic Irreversibility, and Finite-Time Thermodynamics: From Parmenides\u2013Einstein Time-Reversal Symmetry to the Heraclitan Entropic Arrow of Time","display_name":"Temporal Asymmetry, Entropic Irreversibility, and Finite-Time Thermodynamics: From Parmenides\u2013Einstein Time-Reversal Symmetry to the Heraclitan Entropic Arrow of Time","publication_year":2012,"publication_date":"2012-02-28","ids":{"openalex":"https://openalex.org/W1988508167","doi":"https://doi.org/10.3390/e14030407","mag":"1988508167"},"language":"en","primary_location":{"id":"doi:10.3390/e14030407","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e14030407","pdf_url":"https://www.mdpi.com/1099-4300/14/3/407/pdf?version=1424784844","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/1099-4300/14/3/407/pdf?version=1424784844","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033711937","display_name":"Wassim M. Haddad","orcid":"https://orcid.org/0000-0002-4362-3043"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Wassim M. Haddad","raw_affiliation_strings":["The School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA","institution_ids":["https://openalex.org/I130701444"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5033711937"],"corresponding_institution_ids":["https://openalex.org/I130701444"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.6991,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.83255717,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"14","issue":"3","first_page":"407","last_page":"455"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9994000196456909,"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":0.9994000196456909,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9921000003814697,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9861000180244446,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/arrow-of-time","display_name":"Arrow of time","score":0.7620131969451904},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5736601948738098},{"id":"https://openalex.org/keywords/second-law-of-thermodynamics","display_name":"Second law of thermodynamics","score":0.565898597240448},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5598047971725464},{"id":"https://openalex.org/keywords/non-equilibrium-thermodynamics","display_name":"Non-equilibrium thermodynamics","score":0.5431796908378601},{"id":"https://openalex.org/keywords/laws-of-thermodynamics","display_name":"Laws of thermodynamics","score":0.4679250717163086},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4587784707546234},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4572157859802246},{"id":"https://openalex.org/keywords/t-symmetry","display_name":"T-symmetry","score":0.43249568343162537},{"id":"https://openalex.org/keywords/fluctuation-theorem","display_name":"Fluctuation theorem","score":0.4168770909309387},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3568376898765564},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.3565475344657898},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.29068562388420105},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.13581150770187378},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.12022358179092407}],"concepts":[{"id":"https://openalex.org/C14828074","wikidata":"https://www.wikidata.org/wiki/Q186559","display_name":"Arrow of time","level":3,"score":0.7620131969451904},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5736601948738098},{"id":"https://openalex.org/C119820323","wikidata":"https://www.wikidata.org/wiki/Q177045","display_name":"Second law of thermodynamics","level":2,"score":0.565898597240448},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5598047971725464},{"id":"https://openalex.org/C74859849","wikidata":"https://www.wikidata.org/wiki/Q2466686","display_name":"Non-equilibrium thermodynamics","level":2,"score":0.5431796908378601},{"id":"https://openalex.org/C18815010","wikidata":"https://www.wikidata.org/wiki/Q849392","display_name":"Laws of thermodynamics","level":3,"score":0.4679250717163086},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4587784707546234},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4572157859802246},{"id":"https://openalex.org/C152754458","wikidata":"https://www.wikidata.org/wiki/Q142270","display_name":"T-symmetry","level":3,"score":0.43249568343162537},{"id":"https://openalex.org/C108585399","wikidata":"https://www.wikidata.org/wiki/Q900831","display_name":"Fluctuation theorem","level":3,"score":0.4168770909309387},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3568376898765564},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3565475344657898},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.29068562388420105},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.13581150770187378},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.12022358179092407},{"id":"https://openalex.org/C54101563","wikidata":"https://www.wikidata.org/wiki/Q124131","display_name":"Superconductivity","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/e14030407","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e14030407","pdf_url":"https://www.mdpi.com/1099-4300/14/3/407/pdf?version=1424784844","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:8acc471fefe5451abafc74a92a9b2265","is_oa":true,"landing_page_url":"https://doaj.org/article/8acc471fefe5451abafc74a92a9b2265","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 3, Pp 407-455 (2012)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/14/3/407/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e14030407","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 3; Pages: 407-455","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e14030407","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e14030407","pdf_url":"https://www.mdpi.com/1099-4300/14/3/407/pdf?version=1424784844","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":[{"display_name":"Affordable and clean energy","score":0.4699999988079071,"id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W44712423","https://openalex.org/W99253999","https://openalex.org/W157794460","https://openalex.org/W247697463","https://openalex.org/W582868771","https://openalex.org/W594182745","https://openalex.org/W608042531","https://openalex.org/W615876487","https://openalex.org/W645921674","https://openalex.org/W1499871105","https://openalex.org/W1500921805","https://openalex.org/W1598528911","https://openalex.org/W1968212509","https://openalex.org/W1979245447","https://openalex.org/W1988837728","https://openalex.org/W2007696489","https://openalex.org/W2020751453","https://openalex.org/W2064854048","https://openalex.org/W2067265108","https://openalex.org/W2080688746","https://openalex.org/W2091777461","https://openalex.org/W2103264825","https://openalex.org/W2111957799","https://openalex.org/W2123393305","https://openalex.org/W2124439565","https://openalex.org/W2126479355","https://openalex.org/W2128732553","https://openalex.org/W2154608673","https://openalex.org/W2171925382","https://openalex.org/W2316958479","https://openalex.org/W2600589770","https://openalex.org/W2798588639","https://openalex.org/W3021376274","https://openalex.org/W3141151088","https://openalex.org/W3186624155","https://openalex.org/W4238591275","https://openalex.org/W4246455455","https://openalex.org/W4300987473","https://openalex.org/W6630047673"],"related_works":["https://openalex.org/W2949353194","https://openalex.org/W2084426969","https://openalex.org/W4298240961","https://openalex.org/W3091855808","https://openalex.org/W2037105934","https://openalex.org/W2803302763","https://openalex.org/W2783518773","https://openalex.org/W3138427182","https://openalex.org/W2013822926","https://openalex.org/W2501093253"],"abstract_inverted_index":{"In":[0,50],"this":[1],"paper,":[2],"we":[3,32,52,74,100],"combine":[4],"the":[5,41,54,77,91,97,102,119,125],"two":[6],"universalisms":[7],"of":[8,44,56,104,122,128],"thermodynamics":[9],"and":[10,69,111,114,124],"dynamical":[11,17,27,36,66],"systems":[12],"theory":[13,73],"to":[14,85],"develop":[15,33,112],"a":[16,25,34,57],"system":[18,28,37,67,92,98],"formalism":[19],"for":[20,64,107],"classical":[21],"thermodynamics.":[22],"Specifically,":[23],"using":[24,70,96],"compartmental":[26],"energy":[29],"flow":[30],"model":[31,38,80,110],"state-space":[35],"that":[39,76],"captures":[40],"key":[42],"aspects":[43],"thermodynamics,":[45,123],"including":[46],"its":[47],"fundamental":[48],"laws.":[49],"addition,":[51],"establish":[53,101],"existence":[55],"unique,":[58],"continuously":[59],"differentiable":[60],"global":[61],"entropy":[62],"function":[63],"our":[65,108],"model,":[68],"Lyapunov":[71,86],"stability":[72],"show":[75],"proposed":[78],"thermodynamic":[79,109],"has":[81],"finite-time":[82],"convergent":[83],"trajectories":[84],"stable":[87],"equilibria":[88],"determined":[89],"by":[90],"initial":[93],"energies.":[94],"Finally,":[95],"entropy,":[99],"absence":[103],"Poincar\u00e9":[105],"recurrence":[106],"clear":[113],"rigorous":[115],"connections":[116],"between":[117],"irreversibility,":[118],"second":[120],"law":[121],"entropic":[126],"arrow":[127],"time.":[129]},"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":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}