{"id":"https://openalex.org/W4382753149","doi":"https://doi.org/10.3390/e25071012","title":"Ergodic Measure and Potential Control of Anomalous Diffusion","display_name":"Ergodic Measure and Potential Control of Anomalous Diffusion","publication_year":2023,"publication_date":"2023-06-30","ids":{"openalex":"https://openalex.org/W4382753149","doi":"https://doi.org/10.3390/e25071012","pmid":"https://pubmed.ncbi.nlm.nih.gov/37509959"},"language":"en","primary_location":{"id":"doi:10.3390/e25071012","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25071012","pdf_url":"https://www.mdpi.com/1099-4300/25/7/1012/pdf?version=1688133071","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/1099-4300/25/7/1012/pdf?version=1688133071","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109619233","display_name":"Bao Wen","orcid":null},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210116191","display_name":"Institutes of Science and Development","ror":"https://ror.org/02ce9qs13","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210116191"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bao Wen","raw_affiliation_strings":["Institutes of Science and Development, Chinese Academy of Sciences, Beijing 100190, China","School of Public Policy and Management, University of Chinese Academy of Sciences, Beijing 100049, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institutes of Science and Development, Chinese Academy of Sciences, Beijing 100190, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210116191"]},{"raw_affiliation_string":"School of Public Policy and Management, University of Chinese Academy of Sciences, Beijing 100049, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070888216","display_name":"Ming-Gen Li","orcid":"https://orcid.org/0000-0002-4657-0960"},"institutions":[{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ming-Gen Li","raw_affiliation_strings":["Department of Physics, Beijing Normal University, Beijing 100875, China"],"raw_orcid":"https://orcid.org/0000-0002-4657-0960","affiliations":[{"raw_affiliation_string":"Department of Physics, Beijing Normal University, Beijing 100875, China","institution_ids":["https://openalex.org/I25254941"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014194203","display_name":"Jian Liu","orcid":"https://orcid.org/0000-0002-8177-9225"},"institutions":[{"id":"https://openalex.org/I179026463","display_name":"Beijing Technology and Business University","ror":"https://ror.org/013e0zm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I179026463"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jian Liu","raw_affiliation_strings":["Department of Physics, Beijing Technology and Business University, Beijing 100048, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Beijing Technology and Business University, Beijing 100048, China","institution_ids":["https://openalex.org/I179026463"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032850852","display_name":"Jing-Dong Bao","orcid":"https://orcid.org/0000-0002-7871-5861"},"institutions":[{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jing-Dong Bao","raw_affiliation_strings":["Department of Physics, Beijing Normal University, Beijing 100875, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Beijing Normal University, Beijing 100875, China","institution_ids":["https://openalex.org/I25254941"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5032850852"],"corresponding_institution_ids":["https://openalex.org/I25254941"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.7667,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.66580554,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"25","issue":"7","first_page":"1012","last_page":"1012"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9993000030517578,"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9993000030517578,"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9987999796867371,"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":0.998199999332428,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.7589694261550903},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.7143151760101318},{"id":"https://openalex.org/keywords/stationary-ergodic-process","display_name":"Stationary ergodic process","score":0.641620397567749},{"id":"https://openalex.org/keywords/ergodicity","display_name":"Ergodicity","score":0.6215419769287109},{"id":"https://openalex.org/keywords/autocorrelation","display_name":"Autocorrelation","score":0.5993930697441101},{"id":"https://openalex.org/keywords/langevin-equation","display_name":"Langevin equation","score":0.5870729684829712},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5111868977546692},{"id":"https://openalex.org/keywords/anomalous-diffusion","display_name":"Anomalous diffusion","score":0.4999732971191406},{"id":"https://openalex.org/keywords/langevin-dynamics","display_name":"Langevin dynamics","score":0.4563158452510834},{"id":"https://openalex.org/keywords/continuous-time-random-walk","display_name":"Continuous-time random walk","score":0.4501689076423645},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4438704252243042},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4307779371738434},{"id":"https://openalex.org/keywords/observable","display_name":"Observable","score":0.42105263471603394},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.42025846242904663},{"id":"https://openalex.org/keywords/diffusion-process","display_name":"Diffusion process","score":0.4180555045604706},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4081118106842041},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3078174889087677},{"id":"https://openalex.org/keywords/invariant-measure","display_name":"Invariant measure","score":0.2607508897781372},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1934855580329895},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.15290683507919312},{"id":"https://openalex.org/keywords/random-walk","display_name":"Random walk","score":0.10493433475494385}],"concepts":[{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.7589694261550903},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.7143151760101318},{"id":"https://openalex.org/C151424130","wikidata":"https://www.wikidata.org/wiki/Q17123911","display_name":"Stationary ergodic process","level":4,"score":0.641620397567749},{"id":"https://openalex.org/C201779956","wikidata":"https://www.wikidata.org/wiki/Q5426803","display_name":"Ergodicity","level":2,"score":0.6215419769287109},{"id":"https://openalex.org/C5297727","wikidata":"https://www.wikidata.org/wiki/Q786970","display_name":"Autocorrelation","level":2,"score":0.5993930697441101},{"id":"https://openalex.org/C2777577648","wikidata":"https://www.wikidata.org/wiki/Q584537","display_name":"Langevin equation","level":2,"score":0.5870729684829712},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5111868977546692},{"id":"https://openalex.org/C164602753","wikidata":"https://www.wikidata.org/wiki/Q567544","display_name":"Anomalous diffusion","level":3,"score":0.4999732971191406},{"id":"https://openalex.org/C2780004032","wikidata":"https://www.wikidata.org/wiki/Q6485978","display_name":"Langevin dynamics","level":2,"score":0.4563158452510834},{"id":"https://openalex.org/C2777451387","wikidata":"https://www.wikidata.org/wiki/Q18206182","display_name":"Continuous-time random walk","level":3,"score":0.4501689076423645},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4438704252243042},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4307779371738434},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.42105263471603394},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.42025846242904663},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.4180555045604706},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4081118106842041},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3078174889087677},{"id":"https://openalex.org/C115667082","wikidata":"https://www.wikidata.org/wiki/Q4200518","display_name":"Invariant measure","level":3,"score":0.2607508897781372},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1934855580329895},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.15290683507919312},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.10493433475494385},{"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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"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":5,"locations":[{"id":"doi:10.3390/e25071012","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25071012","pdf_url":"https://www.mdpi.com/1099-4300/25/7/1012/pdf?version=1688133071","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:37509959","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/37509959","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:mdpi.com:/1099-4300/25/7/1012/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e25071012","pdf_url":"https://dx.doi.org/10.3390/e25071012","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 25; Issue 7; Pages: 1012","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:10377995","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/10377995","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC10377995/pdf/entropy-25-01012.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:d65d48fc5e064e59b4e4815a24ddce18","is_oa":true,"landing_page_url":"https://doaj.org/article/d65d48fc5e064e59b4e4815a24ddce18","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 25, Iss 7, p 1012 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e25071012","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25071012","pdf_url":"https://www.mdpi.com/1099-4300/25/7/1012/pdf?version=1688133071","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":[{"score":0.7200000286102295,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G6271769291","display_name":"\u5c0f\u7cfb\u7edf\u53cd\u5e38\u6269\u6563\u548c\u5404\u6001\u5386\u7ecf\u7834\u7f3a\u7684\u7406\u8bba\u548c\u5e94\u7528\u7814\u7a76","funder_award_id":"11735005","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4382753149.pdf"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W1973501037","https://openalex.org/W1978754460","https://openalex.org/W1992226679","https://openalex.org/W2003113123","https://openalex.org/W2003113691","https://openalex.org/W2003650759","https://openalex.org/W2009354582","https://openalex.org/W2015888778","https://openalex.org/W2016722695","https://openalex.org/W2019136471","https://openalex.org/W2022977774","https://openalex.org/W2031997608","https://openalex.org/W2033541193","https://openalex.org/W2033742395","https://openalex.org/W2042492157","https://openalex.org/W2048041195","https://openalex.org/W2052126651","https://openalex.org/W2064668837","https://openalex.org/W2065734079","https://openalex.org/W2069617822","https://openalex.org/W2092144432","https://openalex.org/W2102416923","https://openalex.org/W2111271983","https://openalex.org/W2128984571","https://openalex.org/W2150983309","https://openalex.org/W2178399845","https://openalex.org/W2335819537","https://openalex.org/W2797683801","https://openalex.org/W2981922349","https://openalex.org/W3011242050","https://openalex.org/W3022371612","https://openalex.org/W3035497549","https://openalex.org/W3036647916","https://openalex.org/W3080353704","https://openalex.org/W3099401962","https://openalex.org/W3102907556","https://openalex.org/W3104148049","https://openalex.org/W3133438320","https://openalex.org/W3137806046","https://openalex.org/W3198707167","https://openalex.org/W3202704242","https://openalex.org/W4312201962"],"related_works":["https://openalex.org/W1942596836","https://openalex.org/W2066053624","https://openalex.org/W4387774682","https://openalex.org/W3104944153","https://openalex.org/W1971359112","https://openalex.org/W4226271756","https://openalex.org/W2962818245","https://openalex.org/W2155468644","https://openalex.org/W4319312779","https://openalex.org/W4308167194"],"abstract_inverted_index":{"In":[0],"statistical":[1],"mechanics,":[2],"the":[3,7,11,14,44,70,80,86,93,98,103,108,119,124,132,161,169,176,180,191,194,198],"ergodic":[4,83,150],"hypothesis":[5],"(i.e.,":[6],"long-time":[8],"average":[9,46,88,105],"is":[10,38,78,89,129,157],"same":[12],"as":[13,173,175],"ensemble":[15,87],"average)":[16],"accompanying":[17],"anomalous":[18],"diffusion":[19,167,206],"has":[20],"become":[21,74],"a":[22,41,53,75,114,140,144,153],"continuous":[23],"topic":[24],"of":[25,47,82,106,113,171,179,193,201],"research,":[26],"being":[27],"closely":[28],"related":[29],"to":[30,73,92,147,159],"irreversibility":[31],"and":[32,62,110,168,196],"increasing":[33],"entropy.":[34],"While":[35],"measurement":[36],"time":[37,45,104,134],"finite":[39],"for":[40,69,102,139],"given":[42],"process,":[43],"an":[48,148],"observable":[49],"quantity":[50],"might":[51],"be":[52,137],"random":[54],"variable,":[55],"whose":[56],"distribution":[57],"width":[58,101],"narrows":[59],"with":[60,164],"time,":[61],"one":[63],"wonders":[64],"how":[65],"long":[66],"it":[67],"takes":[68],"convergence":[71],"rate":[72],"constant.":[76,94],"This":[77],"also":[79],"premise":[81],"establishment,":[84],"because":[85],"always":[90],"equal":[91],"We":[95],"focus":[96],"on":[97],"time-dependent":[99],"fluctuation":[100],"both":[107],"velocity":[109,126],"kinetic":[111],"energy":[112],"force-free":[115],"particle":[116],"described":[117],"by":[118],"generalized":[120],"Langevin":[121],"equation,":[122],"where":[123],"stationary":[125,145],"autocorrelation":[127],"function":[128],"considered.":[130],"Subsequently,":[131],"shortest":[133],"scale":[135],"can":[136],"estimated":[138],"system":[141],"transferring":[142],"from":[143],"state":[146],"effective":[149],"state.":[151],"Moreover,":[152],"logarithmic":[154,202],"spatial":[155],"potential":[156,203],"used":[158],"modulate":[160],"processes":[162],"associated":[163],"free":[165],"ballistic":[166],"control":[170],"diffusion,":[172],"well":[174],"minimal":[177],"realization":[178],"whole":[181],"power-law":[182],"regime.":[183],"The":[184],"results":[185],"presented":[186],"suggest":[187],"that":[188],"non-ergodicity":[189],"mimics":[190],"sparseness":[192],"medium":[195],"reveals":[197],"unique":[199],"role":[200],"in":[204],"modulating":[205],"behavior.":[207]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":1}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}
