{"id":"https://openalex.org/W2090118902","doi":"https://doi.org/10.3390/e16073605","title":"Entropy Evolution and Uncertainty Estimation with Dynamical Systems","display_name":"Entropy Evolution and Uncertainty Estimation with Dynamical Systems","publication_year":2014,"publication_date":"2014-06-30","ids":{"openalex":"https://openalex.org/W2090118902","doi":"https://doi.org/10.3390/e16073605","mag":"2090118902"},"language":"en","primary_location":{"id":"doi:10.3390/e16073605","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e16073605","pdf_url":"https://www.mdpi.com/1099-4300/16/7/3605/pdf?version=1424785551","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/1099-4300/16/7/3605/pdf?version=1424785551","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000522764","display_name":"X. San Liang","orcid":"https://orcid.org/0000-0001-8472-3211"},"institutions":[{"id":"https://openalex.org/I137867983","display_name":"Central University of Finance and Economics","ror":"https://ror.org/008e3hf02","country_code":"CN","type":"education","lineage":["https://openalex.org/I137867983"]},{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"X. Liang","raw_affiliation_strings":["China Institute for Advanced Study, Central University of Finance and Economics, 39 South College Ave, Beijing 100081, China\u00a0","School of Marine Sciences and School of Mathematics and Statistics, Nanjing University of Information Science and Technology (Nanjing Institute of Meteorology), 219 Ningliu Blvd,Nanjing 210044, China"],"affiliations":[{"raw_affiliation_string":"China Institute for Advanced Study, Central University of Finance and Economics, 39 South College Ave, Beijing 100081, China\u00a0","institution_ids":["https://openalex.org/I137867983"]},{"raw_affiliation_string":"School of Marine Sciences and School of Mathematics and Statistics, Nanjing University of Information Science and Technology (Nanjing Institute of Meteorology), 219 Ningliu Blvd,Nanjing 210044, China","institution_ids":["https://openalex.org/I200845125"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5000522764"],"corresponding_institution_ids":["https://openalex.org/I137867983","https://openalex.org/I200845125"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.7171,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.7197328,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"16","issue":"7","first_page":"3605","last_page":"3634"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9988999962806702,"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":0.9988999962806702,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9965000152587891,"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/T13377","display_name":"Ecosystem dynamics and resilience","score":0.9900000095367432,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5881687998771667},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5622856616973877},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5511974692344666},{"id":"https://openalex.org/keywords/phase-space","display_name":"Phase space","score":0.5125865340232849},{"id":"https://openalex.org/keywords/lorenz-system","display_name":"Lorenz system","score":0.5035235285758972},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.48508989810943604},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.45778030157089233},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45345282554626465},{"id":"https://openalex.org/keywords/conserved-quantity","display_name":"Conserved quantity","score":0.4485253393650055},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.44832366704940796},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33797961473464966},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33546268939971924},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21333253383636475},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19306892156600952},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12179014086723328},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.12164363265037537}],"concepts":[{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5881687998771667},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5622856616973877},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5511974692344666},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.5125865340232849},{"id":"https://openalex.org/C151510863","wikidata":"https://www.wikidata.org/wiki/Q899844","display_name":"Lorenz system","level":3,"score":0.5035235285758972},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.48508989810943604},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.45778030157089233},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45345282554626465},{"id":"https://openalex.org/C71914180","wikidata":"https://www.wikidata.org/wiki/Q1071013","display_name":"Conserved quantity","level":2,"score":0.4485253393650055},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.44832366704940796},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33797961473464966},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33546268939971924},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21333253383636475},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19306892156600952},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12179014086723328},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.12164363265037537},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/e16073605","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e16073605","pdf_url":"https://www.mdpi.com/1099-4300/16/7/3605/pdf?version=1424785551","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:6eaae6d52c1043df8be5c2b30d3e2093","is_oa":true,"landing_page_url":"https://doaj.org/article/6eaae6d52c1043df8be5c2b30d3e2093","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 16, Iss 7, Pp 3605-3634 (2014)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/16/7/3605/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e16073605","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 16; Issue 7; Pages: 3605-3634","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e16073605","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e16073605","pdf_url":"https://www.mdpi.com/1099-4300/16/7/3605/pdf?version=1424785551","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2090118902.pdf","grobid_xml":"https://content.openalex.org/works/W2090118902.grobid-xml"},"referenced_works_count":54,"referenced_works":["https://openalex.org/W1524247963","https://openalex.org/W1540810403","https://openalex.org/W1615338691","https://openalex.org/W1969471372","https://openalex.org/W1969534246","https://openalex.org/W1971715144","https://openalex.org/W1972639576","https://openalex.org/W1987330150","https://openalex.org/W1995875735","https://openalex.org/W2000530301","https://openalex.org/W2001673819","https://openalex.org/W2003068273","https://openalex.org/W2005541362","https://openalex.org/W2024794407","https://openalex.org/W2030038024","https://openalex.org/W2032558547","https://openalex.org/W2042788778","https://openalex.org/W2057895204","https://openalex.org/W2061097716","https://openalex.org/W2070545404","https://openalex.org/W2072319095","https://openalex.org/W2073696559","https://openalex.org/W2078901052","https://openalex.org/W2086239189","https://openalex.org/W2095459380","https://openalex.org/W2099111195","https://openalex.org/W2109775438","https://openalex.org/W2111804884","https://openalex.org/W2125589218","https://openalex.org/W2135810406","https://openalex.org/W2139139723","https://openalex.org/W2141702337","https://openalex.org/W2164901548","https://openalex.org/W2165198298","https://openalex.org/W2167921997","https://openalex.org/W2173296550","https://openalex.org/W2173363853","https://openalex.org/W2253797267","https://openalex.org/W2333143535","https://openalex.org/W2624590440","https://openalex.org/W3015681226","https://openalex.org/W3098084401","https://openalex.org/W4232473186","https://openalex.org/W4232726482","https://openalex.org/W4247323812","https://openalex.org/W4301267015","https://openalex.org/W4307755210","https://openalex.org/W6636267314","https://openalex.org/W6647201127","https://openalex.org/W6656656079","https://openalex.org/W6658723161","https://openalex.org/W6665689369","https://openalex.org/W6667808436","https://openalex.org/W6670320693"],"related_works":["https://openalex.org/W2780647614","https://openalex.org/W1967212527","https://openalex.org/W2061794113","https://openalex.org/W2377864929","https://openalex.org/W2376785386","https://openalex.org/W2090047826","https://openalex.org/W2594130944","https://openalex.org/W2095860056","https://openalex.org/W2351359734","https://openalex.org/W2122669027"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,53,106,119,131,157,163],"comprehensive":[4],"introduction":[5],"and":[6,17,45,49,75,97,105,144,167,177],"systematic":[7],"derivation":[8],"of":[9,22,38,56,63,71,82,136,184,189],"the":[10,27,36,50,57,61,69,80,102,113,134,137,148,174,178,187,202],"evolutionary":[11],"equations":[12],"for":[13],"absolute":[14],"entropy":[15,19],"H":[16,44,116,126],"relative":[18],"D,":[20],"some":[21],"which":[23],"exist":[24],"sporadically":[25],"in":[26,29,60,186],"literature":[28],"different":[30,33],"forms":[31],"under":[32],"subjects,":[34],"within":[35],"framework":[37],"dynamical":[39],"systems.":[40],"In":[41,112],"general,":[42],"both":[43],"D":[46,76],"are":[47,92,182],"dissipated,":[48],"dissipation":[51],"bears":[52],"form":[54],"reminiscent":[55],"Fisher":[58],"information;":[59],"absence":[62],"stochasticity,":[64],"dH/dt":[65],"is":[66,87,153],"connected":[67],"to":[68,99,156],"rate":[70,121],"phase":[72],"space":[73],"expansion,":[74],"stays":[77],"invariant,":[78],"i.e.,":[79],"separation":[81],"two":[83],"probability":[84],"density":[85],"functions":[86],"always":[88],"conserved.":[89],"These":[90],"formulas":[91],"validated":[93],"with":[94,101,122],"linear":[95],"systems,":[96],"put":[98],"application":[100],"Lorenz":[103,114,175],"system":[104,176,181],"large-dimensional":[107],"stochastic":[108,149,179],"quasi-geostrophic":[109],"flow":[110,150,180],"problem.":[111],"case,":[115],"falls":[117],"at":[118],"constant":[120],"time,":[123],"implying":[124],"that":[125],"will":[127],"eventually":[128],"become":[129],"negative,":[130],"situation":[132],"beyond":[133],"capability":[135],"commonly":[138],"used":[139],"computational":[140],"technique":[141],"like":[142],"coarse-graining":[143],"bin":[145],"counting.":[146],"For":[147],"problem,":[151],"it":[152],"first":[154],"reduced":[155,164],"computationally":[158],"tractable":[159],"low-dimensional":[160],"system,":[161],"using":[162],"model":[165],"approach,":[166],"then":[168],"handled":[169],"through":[170],"ensemble":[171],"prediction.":[172],"Both":[173],"examples":[183],"self-organization":[185,203],"light":[188],"uncertainty":[190],"reduction.":[191],"The":[192],"latter":[193],"particularly":[194],"shows":[195],"that,":[196],"sometimes":[197],"stochasticity":[198],"may":[199],"actually":[200],"enhance":[201],"process.":[204]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":3}],"updated_date":"2026-03-06T13:50:29.536080","created_date":"2025-10-10T00:00:00"}