{"id":"https://openalex.org/W4401418943","doi":"https://doi.org/10.3390/e26080673","title":"Generalized Kinetic Equations with Fractional Time-Derivative and Nonlinear Diffusion: H-Theorem and Entropy","display_name":"Generalized Kinetic Equations with Fractional Time-Derivative and Nonlinear Diffusion: H-Theorem and Entropy","publication_year":2024,"publication_date":"2024-08-08","ids":{"openalex":"https://openalex.org/W4401418943","doi":"https://doi.org/10.3390/e26080673","pmid":"https://pubmed.ncbi.nlm.nih.gov/39202143"},"language":"en","primary_location":{"id":"doi:10.3390/e26080673","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26080673","pdf_url":null,"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://doi.org/10.3390/e26080673","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060481487","display_name":"E. K. Lenzi","orcid":"https://orcid.org/0000-0003-3853-1790"},"institutions":[{"id":"https://openalex.org/I4210125245","display_name":"Centro Brasileiro de Pesquisas F\u00edsicas","ror":"https://ror.org/02wnmk332","country_code":"BR","type":"facility","lineage":["https://openalex.org/I4210125245","https://openalex.org/I4210151455"]},{"id":"https://openalex.org/I68207295","display_name":"Universidade Estadual de Ponta Grossa","ror":"https://ror.org/027s08w94","country_code":"BR","type":"education","lineage":["https://openalex.org/I68207295"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Ervin K. Lenzi","raw_affiliation_strings":["Departamento de F\u00edsica, Universidade Estadual de Ponta Grossa, Ponta Grossa 84030-900, PR, Brazil","National Institute of Science and Technology for Complex Systems, Centro Brasileiro de Pesquisas F\u00edsicas, Rio de Janeiro 22290-180, RJ, Brazil"],"raw_orcid":"https://orcid.org/0000-0003-3853-1790","affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica, Universidade Estadual de Ponta Grossa, Ponta Grossa 84030-900, PR, Brazil","institution_ids":["https://openalex.org/I68207295"]},{"raw_affiliation_string":"National Institute of Science and Technology for Complex Systems, Centro Brasileiro de Pesquisas F\u00edsicas, Rio de Janeiro 22290-180, RJ, Brazil","institution_ids":["https://openalex.org/I4210125245"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056294264","display_name":"M. P. Rosseto","orcid":"https://orcid.org/0000-0001-6158-3068"},"institutions":[{"id":"https://openalex.org/I68207295","display_name":"Universidade Estadual de Ponta Grossa","ror":"https://ror.org/027s08w94","country_code":"BR","type":"education","lineage":["https://openalex.org/I68207295"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Michely P. Rosseto","raw_affiliation_strings":["Departamento de F\u00edsica, Universidade Estadual de Ponta Grossa, Ponta Grossa 84030-900, PR, Brazil"],"raw_orcid":"https://orcid.org/0000-0001-6158-3068","affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica, Universidade Estadual de Ponta Grossa, Ponta Grossa 84030-900, PR, Brazil","institution_ids":["https://openalex.org/I68207295"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091659752","display_name":"Derik W. Gryczak","orcid":"https://orcid.org/0000-0002-5883-6404"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Derik W. Gryczak","raw_affiliation_strings":["Independent Researcher, Irati 84507-012, PR, Brazil"],"raw_orcid":"https://orcid.org/0000-0002-5883-6404","affiliations":[{"raw_affiliation_string":"Independent Researcher, Irati 84507-012, PR, Brazil","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006098704","display_name":"L. R. Evangelista","orcid":"https://orcid.org/0000-0001-7202-1386"},"institutions":[{"id":"https://openalex.org/I123443094","display_name":"Universidade Estadual de Maring\u00e1","ror":"https://ror.org/04bqqa360","country_code":"BR","type":"education","lineage":["https://openalex.org/I123443094"]},{"id":"https://openalex.org/I149461666","display_name":"Ca' Foscari University of Venice","ror":"https://ror.org/04yzxz566","country_code":"IT","type":"education","lineage":["https://openalex.org/I149461666"]},{"id":"https://openalex.org/I4210149433","display_name":"Institute for Complex Systems","ror":"https://ror.org/05rcgef49","country_code":"IT","type":"facility","lineage":["https://openalex.org/I4210149433","https://openalex.org/I4210155236"]}],"countries":["BR","IT"],"is_corresponding":false,"raw_author_name":"Luiz R. Evangelista","raw_affiliation_strings":["Departamento de F\u00edsica, Universidade Estadual de Maring\u00e1, Maring\u00e1 87020-900, PR, Brazil","Department of Molecular Science and Nanosystems, Ca\u2019Foscari University of Venice, Via Torino, 155, 30172 Mestre, Italy","Istituto dei Sistemi Complessi (ISC\u2013CNR), Via dei Taurini, 19, 00185 Rome, Italy","Department of Molecular Science and Nanosystems, Ca'Foscari University of Venice, Via Torino, 155, 30172 Mestre, Italy"],"raw_orcid":"https://orcid.org/0000-0001-7202-1386","affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica, Universidade Estadual de Maring\u00e1, Maring\u00e1 87020-900, PR, Brazil","institution_ids":["https://openalex.org/I123443094"]},{"raw_affiliation_string":"Department of Molecular Science and Nanosystems, Ca\u2019Foscari University of Venice, Via Torino, 155, 30172 Mestre, Italy","institution_ids":["https://openalex.org/I149461666"]},{"raw_affiliation_string":"Istituto dei Sistemi Complessi (ISC\u2013CNR), Via dei Taurini, 19, 00185 Rome, Italy","institution_ids":["https://openalex.org/I4210149433"]},{"raw_affiliation_string":"Department of Molecular Science and Nanosystems, Ca'Foscari University of Venice, Via Torino, 155, 30172 Mestre, Italy","institution_ids":["https://openalex.org/I149461666"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020648609","display_name":"L. R. da Silva","orcid":"https://orcid.org/0000-0002-6875-1965"},"institutions":[{"id":"https://openalex.org/I35046152","display_name":"Universidade Federal do Rio Grande do Norte","ror":"https://ror.org/04wn09761","country_code":"BR","type":"education","lineage":["https://openalex.org/I35046152"]},{"id":"https://openalex.org/I4210125245","display_name":"Centro Brasileiro de Pesquisas F\u00edsicas","ror":"https://ror.org/02wnmk332","country_code":"BR","type":"facility","lineage":["https://openalex.org/I4210125245","https://openalex.org/I4210151455"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Luciano R. da Silva","raw_affiliation_strings":["Departamento de F\u00edsica, Universidade Federal do Rio Grande do Norte, Natal 59078-900, RN, Brazil","National Institute of Science and Technology for Complex Systems, Centro Brasileiro de Pesquisas F\u00edsicas, Rio de Janeiro 22290-180, RJ, Brazil"],"raw_orcid":"https://orcid.org/0000-0002-6875-1965","affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica, Universidade Federal do Rio Grande do Norte, Natal 59078-900, RN, Brazil","institution_ids":["https://openalex.org/I35046152"]},{"raw_affiliation_string":"National Institute of Science and Technology for Complex Systems, Centro Brasileiro de Pesquisas F\u00edsicas, Rio de Janeiro 22290-180, RJ, Brazil","institution_ids":["https://openalex.org/I4210125245"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086207974","display_name":"Marcelo Kaminski Lenzi","orcid":"https://orcid.org/0000-0002-0103-9017"},"institutions":[{"id":"https://openalex.org/I52418104","display_name":"Universidade Federal do Paran\u00e1","ror":"https://ror.org/05syd6y78","country_code":"BR","type":"education","lineage":["https://openalex.org/I52418104"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Marcelo K. Lenzi","raw_affiliation_strings":["Departamento de Engenharia Qu\u00edmica, Universidade Federal do Paran\u00e1, Curitiba 80060-000, PR, Brazil"],"raw_orcid":"https://orcid.org/0000-0002-0103-9017","affiliations":[{"raw_affiliation_string":"Departamento de Engenharia Qu\u00edmica, Universidade Federal do Paran\u00e1, Curitiba 80060-000, PR, Brazil","institution_ids":["https://openalex.org/I52418104"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024867698","display_name":"Rafael S. Zola","orcid":"https://orcid.org/0000-0003-4930-5262"},"institutions":[{"id":"https://openalex.org/I1283613182","display_name":"Universidade Tecnol\u00f3gica Federal do Paran\u00e1","ror":"https://ror.org/002v2kq79","country_code":"BR","type":"education","lineage":["https://openalex.org/I1283613182"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Rafael S. Zola","raw_affiliation_strings":["Department of Physics, Universidade Tecnol\u00f3gica Federal do Paran\u00e1, Apucarana 86812-460, PR, Brazil"],"raw_orcid":"https://orcid.org/0000-0003-4930-5262","affiliations":[{"raw_affiliation_string":"Department of Physics, Universidade Tecnol\u00f3gica Federal do Paran\u00e1, Apucarana 86812-460, PR, Brazil","institution_ids":["https://openalex.org/I1283613182"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5060481487"],"corresponding_institution_ids":["https://openalex.org/I4210125245","https://openalex.org/I68207295"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.0734,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.74700704,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"26","issue":"8","first_page":"673","last_page":"673"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9973000288009644,"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/T11565","display_name":"Thermoelastic and Magnetoelastic Phenomena","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/mathematics","display_name":"Mathematics","score":0.6636940240859985},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5637053847312927},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5341671109199524},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4779098927974701},{"id":"https://openalex.org/keywords/h-theorem","display_name":"H-theorem","score":0.471773624420166},{"id":"https://openalex.org/keywords/anomalous-diffusion","display_name":"Anomalous diffusion","score":0.46864551305770874},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45219171047210693},{"id":"https://openalex.org/keywords/kinetic-energy","display_name":"Kinetic energy","score":0.44805124402046204},{"id":"https://openalex.org/keywords/time-derivative","display_name":"Time derivative","score":0.4399757385253906},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3839814364910126},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3734278678894043},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3365769684314728},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.24968785047531128},{"id":"https://openalex.org/keywords/binary-entropy-function","display_name":"Binary entropy function","score":0.2482713758945465},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.24641823768615723},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.22969192266464233},{"id":"https://openalex.org/keywords/maximum-entropy-thermodynamics","display_name":"Maximum entropy thermodynamics","score":0.20943796634674072},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.13925489783287048},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11701557040214539},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10434579849243164},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08049216866493225}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6636940240859985},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5637053847312927},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5341671109199524},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4779098927974701},{"id":"https://openalex.org/C179434709","wikidata":"https://www.wikidata.org/wiki/Q899853","display_name":"H-theorem","level":5,"score":0.471773624420166},{"id":"https://openalex.org/C164602753","wikidata":"https://www.wikidata.org/wiki/Q567544","display_name":"Anomalous diffusion","level":3,"score":0.46864551305770874},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45219171047210693},{"id":"https://openalex.org/C135889238","wikidata":"https://www.wikidata.org/wiki/Q46276","display_name":"Kinetic energy","level":2,"score":0.44805124402046204},{"id":"https://openalex.org/C17685861","wikidata":"https://www.wikidata.org/wiki/Q6960532","display_name":"Time derivative","level":2,"score":0.4399757385253906},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3839814364910126},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3734278678894043},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3365769684314728},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24968785047531128},{"id":"https://openalex.org/C44415725","wikidata":"https://www.wikidata.org/wiki/Q4913893","display_name":"Binary entropy function","level":3,"score":0.2482713758945465},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.24641823768615723},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.22969192266464233},{"id":"https://openalex.org/C49775889","wikidata":"https://www.wikidata.org/wiki/Q6795896","display_name":"Maximum entropy thermodynamics","level":4,"score":0.20943796634674072},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.13925489783287048},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11701557040214539},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10434579849243164},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08049216866493225},{"id":"https://openalex.org/C3017618536","wikidata":"https://www.wikidata.org/wiki/Q304994","display_name":"Innovation diffusion","level":2,"score":0.0},{"id":"https://openalex.org/C56739046","wikidata":"https://www.wikidata.org/wiki/Q192060","display_name":"Knowledge management","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e26080673","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26080673","pdf_url":null,"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:39202143","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/39202143","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:pubmedcentral.nih.gov:11354171","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/11354171","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC11354171/pdf/entropy-26-00673.pdf","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"},{"id":"pmh:oai:doaj.org/article:4d40c6384f7f4645afec1753e9711825","is_oa":true,"landing_page_url":"https://doaj.org/article/4d40c6384f7f4645afec1753e9711825","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 26, Iss 8, p 673 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e26080673","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26080673","pdf_url":null,"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/G3849460185","display_name":null,"funder_award_id":"301715/2022-0","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G4503065587","display_name":null,"funder_award_id":"304634/2020-4","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G8259684238","display_name":null,"funder_award_id":"FAPESP\u20142014/50983-3","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G8798373047","display_name":null,"funder_award_id":"FAPESP\u20142014/50983-3","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"}],"funders":[{"id":"https://openalex.org/F4320320997","display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","ror":"https://ror.org/02ddkpn78"},{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":62,"referenced_works":["https://openalex.org/W101914685","https://openalex.org/W285310959","https://openalex.org/W1873431535","https://openalex.org/W1968586469","https://openalex.org/W1970119229","https://openalex.org/W1973449286","https://openalex.org/W1977265570","https://openalex.org/W1978079922","https://openalex.org/W1978824346","https://openalex.org/W1980752513","https://openalex.org/W1983874169","https://openalex.org/W1983930467","https://openalex.org/W1988097453","https://openalex.org/W1988468031","https://openalex.org/W1997805537","https://openalex.org/W1999873841","https://openalex.org/W2026946703","https://openalex.org/W2032793676","https://openalex.org/W2040183387","https://openalex.org/W2041964490","https://openalex.org/W2045350842","https://openalex.org/W2052112788","https://openalex.org/W2061358965","https://openalex.org/W2075357366","https://openalex.org/W2081794772","https://openalex.org/W2084058002","https://openalex.org/W2088338349","https://openalex.org/W2089852843","https://openalex.org/W2093046328","https://openalex.org/W2108797601","https://openalex.org/W2111271983","https://openalex.org/W2126482060","https://openalex.org/W2141699138","https://openalex.org/W2161349314","https://openalex.org/W2277514911","https://openalex.org/W2327219438","https://openalex.org/W2496653833","https://openalex.org/W2507685292","https://openalex.org/W2556784265","https://openalex.org/W2584641334","https://openalex.org/W2589470502","https://openalex.org/W2612857253","https://openalex.org/W2625936354","https://openalex.org/W2786288410","https://openalex.org/W2963641381","https://openalex.org/W3023623741","https://openalex.org/W3101064457","https://openalex.org/W3137864905","https://openalex.org/W3156496011","https://openalex.org/W3158716607","https://openalex.org/W3159409442","https://openalex.org/W3198488549","https://openalex.org/W3199693888","https://openalex.org/W4224214005","https://openalex.org/W4287843537","https://openalex.org/W4290720665","https://openalex.org/W4300825577","https://openalex.org/W4386895109","https://openalex.org/W4396695212","https://openalex.org/W6639635870","https://openalex.org/W6730176618","https://openalex.org/W6771239883"],"related_works":["https://openalex.org/W2528667048","https://openalex.org/W2099172367","https://openalex.org/W2954522738","https://openalex.org/W2501432554","https://openalex.org/W2161513111","https://openalex.org/W1965190038","https://openalex.org/W912076904","https://openalex.org/W2106244600","https://openalex.org/W1989611874","https://openalex.org/W4287250104"],"abstract_inverted_index":{"We":[0,37],"investigate":[1,55],"the":[2,20,34,39],"H-theorem":[3,21],"for":[4,58],"a":[5,68],"class":[6,70],"of":[7,71],"generalized":[8],"kinetic":[9],"equations":[10,60],"with":[11,74],"fractional":[12],"time-derivative,":[13],"hyperbolic":[14],"term,":[15],"and":[16,46,64,77],"nonlinear":[17],"diffusion.":[18],"When":[19],"is":[22],"satisfied,":[23],"we":[24,54],"demonstrate":[25],"that":[26,48],"different":[27],"entropic":[28],"forms":[29],"may":[30],"emerge":[31],"due":[32],"to":[33,43],"equation's":[35],"nonlinearity.":[36],"obtain":[38],"entropy":[40],"production":[41],"related":[42],"these":[44,59],"entropies":[45],"show":[47],"its":[49],"form":[50],"remains":[51],"invariant.":[52],"Furthermore,":[53],"some":[56],"behaviors":[57,72],"from":[61],"both":[62],"numerical":[63],"analytical":[65],"perspectives,":[66],"showing":[67],"large":[69],"connected":[73],"anomalous":[75],"diffusion":[76],"their":[78],"effects":[79],"on":[80],"entropy.":[81]},"counts_by_year":[{"year":2025,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}