{"id":"https://openalex.org/W2888937769","doi":"https://doi.org/10.3390/e20090658","title":"Thermodynamics of Superdiffusion Generated by L\u00e9vy\u2013Wiener Fluctuating Forces","display_name":"Thermodynamics of Superdiffusion Generated by L\u00e9vy\u2013Wiener Fluctuating Forces","publication_year":2018,"publication_date":"2018-08-31","ids":{"openalex":"https://openalex.org/W2888937769","doi":"https://doi.org/10.3390/e20090658","mag":"2888937769","pmid":"https://pubmed.ncbi.nlm.nih.gov/33265747"},"language":"en","primary_location":{"id":"doi:10.3390/e20090658","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e20090658","pdf_url":"https://www.mdpi.com/1099-4300/20/9/658/pdf?version=1535719155","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/1099-4300/20/9/658/pdf?version=1535719155","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051558700","display_name":"\u0141ukasz Ku\u015bmierz","orcid":"https://orcid.org/0000-0003-3090-2550"},"institutions":[{"id":"https://openalex.org/I2800939219","display_name":"RIKEN Center for Brain Science","ror":"https://ror.org/04j1n1c04","country_code":"JP","type":"facility","lineage":["https://openalex.org/I2800939219","https://openalex.org/I4210110652"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"\u0141ukasz Ku\u015bmierz","raw_affiliation_strings":["Laboratory for Neural Computation and Adaptation, RIKEN Center for Brain Science, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory for Neural Computation and Adaptation, RIKEN Center for Brain Science, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan","institution_ids":["https://openalex.org/I2800939219"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079744597","display_name":"Bart\u0142omiej Dybiec","orcid":"https://orcid.org/0000-0002-6540-3906"},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]},{"id":"https://openalex.org/I4210086947","display_name":"Institute of Physics","ror":"https://ror.org/000sfad56","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210086947","https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Bart\u0142omiej Dybiec","raw_affiliation_strings":["Marian Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Center, Jagiellonian University, ul. S. \u0141ojasiewicza 11, 30-348 Krak\u00f3w, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Marian Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Center, Jagiellonian University, ul. S. \u0141ojasiewicza 11, 30-348 Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746","https://openalex.org/I4210086947"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006455804","display_name":"Ewa Gudowska\u2013Nowak","orcid":"https://orcid.org/0000-0001-5604-094X"},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]},{"id":"https://openalex.org/I4210086947","display_name":"Institute of Physics","ror":"https://ror.org/000sfad56","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210086947","https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Ewa Gudowska-Nowak","raw_affiliation_strings":["Marian Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Center, Jagiellonian University, ul. S. \u0141ojasiewicza 11, 30-348 Krak\u00f3w, Poland"],"raw_orcid":"https://orcid.org/0000-0001-5604-094X","affiliations":[{"raw_affiliation_string":"Marian Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Center, Jagiellonian University, ul. S. \u0141ojasiewicza 11, 30-348 Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746","https://openalex.org/I4210086947"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5006455804"],"corresponding_institution_ids":["https://openalex.org/I126596746","https://openalex.org/I4210086947"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.0756,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.77373482,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"20","issue":"9","first_page":"658","last_page":"658"},"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/T13187","display_name":"Diffusion and Search Dynamics","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","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"}}],"keywords":[{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.6775985956192017},{"id":"https://openalex.org/keywords/brownian-motion","display_name":"Brownian motion","score":0.5887293219566345},{"id":"https://openalex.org/keywords/stationary-state","display_name":"Stationary state","score":0.5563445091247559},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4913715422153473},{"id":"https://openalex.org/keywords/white-noise","display_name":"White noise","score":0.4840792715549469},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.4609648883342743},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.45929425954818726},{"id":"https://openalex.org/keywords/stationary-distribution","display_name":"Stationary distribution","score":0.4586280882358551},{"id":"https://openalex.org/keywords/langevin-equation","display_name":"Langevin equation","score":0.4534105062484741},{"id":"https://openalex.org/keywords/wiener-process","display_name":"Wiener process","score":0.44445598125457764},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.43536341190338135},{"id":"https://openalex.org/keywords/detailed-balance","display_name":"Detailed balance","score":0.431816041469574},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4252296984195709},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.3648653030395508},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2988249659538269},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1581789255142212}],"concepts":[{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.6775985956192017},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.5887293219566345},{"id":"https://openalex.org/C47458137","wikidata":"https://www.wikidata.org/wiki/Q911951","display_name":"Stationary state","level":2,"score":0.5563445091247559},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4913715422153473},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.4840792715549469},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.4609648883342743},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.45929425954818726},{"id":"https://openalex.org/C98951983","wikidata":"https://www.wikidata.org/wiki/Q7604341","display_name":"Stationary distribution","level":3,"score":0.4586280882358551},{"id":"https://openalex.org/C2777577648","wikidata":"https://www.wikidata.org/wiki/Q584537","display_name":"Langevin equation","level":2,"score":0.4534105062484741},{"id":"https://openalex.org/C60391097","wikidata":"https://www.wikidata.org/wiki/Q1056809","display_name":"Wiener process","level":2,"score":0.44445598125457764},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.43536341190338135},{"id":"https://openalex.org/C135694725","wikidata":"https://www.wikidata.org/wiki/Q1201087","display_name":"Detailed balance","level":2,"score":0.431816041469574},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4252296984195709},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.3648653030395508},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2988249659538269},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1581789255142212},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.3390/e20090658","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e20090658","pdf_url":"https://www.mdpi.com/1099-4300/20/9/658/pdf?version=1535719155","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:33265747","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33265747","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:ruj.uj.edu.pl:item/58593","is_oa":true,"landing_page_url":"https://ruj.uj.edu.pl/xmlui/handle/item/58593","pdf_url":"http://ruj.uj.edu.pl/bitstreams/f40c6186-acc3-4e06-8392-fb39fa947b4b/download","source":{"id":"https://openalex.org/S4306401249","display_name":"Jagiellonian University Repository (Jagiellonian University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I126596746","host_organization_name":"Jagiellonian University","host_organization_lineage":["https://openalex.org/I126596746"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:6422b5c0-5693-47ba-aeae-7f0b82665759/oai:ruj.uj.edu.pl:item/58593","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401248","display_name":"Jagiellonian University Repository (Jagiellonian University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I126596746","host_organization_name":"Jagiellonian University","host_organization_lineage":["https://openalex.org/I126596746"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:doaj.org/article:a100e08e81934dda9d448cc12c629351","is_oa":true,"landing_page_url":"https://doaj.org/article/a100e08e81934dda9d448cc12c629351","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 20, Iss 9, p 658 (2018)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/20/9/658/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e20090658","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","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7513181","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7513181","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/e20090658","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e20090658","pdf_url":"https://www.mdpi.com/1099-4300/20/9/658/pdf?version=1535719155","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/W2888937769.pdf","grobid_xml":"https://content.openalex.org/works/W2888937769.grobid-xml"},"referenced_works_count":88,"referenced_works":["https://openalex.org/W44637910","https://openalex.org/W1518742351","https://openalex.org/W1712132062","https://openalex.org/W1816275442","https://openalex.org/W1901964486","https://openalex.org/W1935394376","https://openalex.org/W1970283086","https://openalex.org/W1977079737","https://openalex.org/W1977360274","https://openalex.org/W1985758640","https://openalex.org/W1986091197","https://openalex.org/W1987441107","https://openalex.org/W1990075943","https://openalex.org/W2000273341","https://openalex.org/W2003214293","https://openalex.org/W2003982596","https://openalex.org/W2004474342","https://openalex.org/W2005039310","https://openalex.org/W2008327242","https://openalex.org/W2009619854","https://openalex.org/W2011343927","https://openalex.org/W2012021517","https://openalex.org/W2012029574","https://openalex.org/W2018674686","https://openalex.org/W2019592129","https://openalex.org/W2020698062","https://openalex.org/W2021239100","https://openalex.org/W2026305126","https://openalex.org/W2030181230","https://openalex.org/W2040608308","https://openalex.org/W2040675064","https://openalex.org/W2046660045","https://openalex.org/W2046833142","https://openalex.org/W2049078897","https://openalex.org/W2054787859","https://openalex.org/W2055922934","https://openalex.org/W2056284729","https://openalex.org/W2085440349","https://openalex.org/W2085874333","https://openalex.org/W2087627047","https://openalex.org/W2091704019","https://openalex.org/W2093744628","https://openalex.org/W2099069893","https://openalex.org/W2102277728","https://openalex.org/W2106938311","https://openalex.org/W2107988867","https://openalex.org/W2111271983","https://openalex.org/W2117425670","https://openalex.org/W2125418826","https://openalex.org/W2128577635","https://openalex.org/W2137864581","https://openalex.org/W2164031620","https://openalex.org/W2168917328","https://openalex.org/W2170486501","https://openalex.org/W2268968240","https://openalex.org/W2291221954","https://openalex.org/W2316244279","https://openalex.org/W2316917456","https://openalex.org/W2317436645","https://openalex.org/W2327229416","https://openalex.org/W2329475110","https://openalex.org/W2346123201","https://openalex.org/W2400030893","https://openalex.org/W2413779870","https://openalex.org/W2472557287","https://openalex.org/W2482990380","https://openalex.org/W2486387419","https://openalex.org/W2492855992","https://openalex.org/W2509835205","https://openalex.org/W2606657960","https://openalex.org/W2611011638","https://openalex.org/W2621316318","https://openalex.org/W2761502696","https://openalex.org/W2943195202","https://openalex.org/W2951189555","https://openalex.org/W3099023905","https://openalex.org/W3099119867","https://openalex.org/W3100794497","https://openalex.org/W3100916398","https://openalex.org/W3100922914","https://openalex.org/W3104589912","https://openalex.org/W3104978828","https://openalex.org/W3125246470","https://openalex.org/W3141588430","https://openalex.org/W3215113436","https://openalex.org/W4231695981","https://openalex.org/W4388167314","https://openalex.org/W6765995216"],"related_works":["https://openalex.org/W2033050283","https://openalex.org/W1974240558","https://openalex.org/W2368309130","https://openalex.org/W2105576424","https://openalex.org/W2576847637","https://openalex.org/W2801640167","https://openalex.org/W2066988799","https://openalex.org/W2041677292","https://openalex.org/W1568619890","https://openalex.org/W1532813632"],"abstract_inverted_index":{"Scale":[0],"free":[1],"L\u00e9vy":[2,69],"motion":[3],"is":[4,58,65,83,114],"a":[5,55,79,117],"generalized":[6],"analogue":[7],"of":[8,18,51,74,89,127,131,135,145],"the":[9,16,49,87,95,100,107,128,132,136,142,146],"Wiener":[10],"process.":[11],"Its":[12],"time":[13],"derivative":[14],"extends":[15],"notion":[17],"\"white":[19],"noise\"":[20],"to":[21,33],"non-Gaussian":[22],"noise":[23,64],"sources,":[24],"and":[25,63,121,138],"as":[26],"such,":[27],"it":[28],"has":[29],"been":[30],"widely":[31],"used":[32],"model":[34],"natural":[35],"signal":[36],"variations":[37],"described":[38],"by":[39,60,67,86,116],"an":[40,52],"overdamped":[41],"Langevin":[42],"stochastic":[43],"differential":[44],"equation.":[45],"Here,":[46],"we":[47],"consider":[48],"dynamics":[50],"archetypal":[53],"model:":[54],"Brownian-like":[56],"particle":[57],"driven":[59],"external":[61,152],"forces,":[62],"represented":[66],"uncorrelated":[68],"fluctuations.":[70],"An":[71],"unperturbed":[72],"system":[73,137],"that":[75,94],"form":[76,144],"eventually":[77],"attains":[78],"steady":[80],"state":[81,113,134],"which":[82],"uniquely":[84],"determined":[85],"set":[88],"parameter":[90],"values.":[91],"We":[92,124],"show":[93],"analyzed":[96],"Markov":[97],"process":[98],"with":[99],"stability":[101],"index":[102],"\u03b1":[103],"<":[104],"2":[105],"violates":[106],"detailed":[108],"balance,":[109],"i.e.,":[110],"its":[111,139],"stationary":[112,118,133],"quantified":[115],"probability":[119],"density":[120],"nonvanishing":[122],"current.":[123],"discuss":[125],"consequences":[126],"non-Gibbsian":[129],"character":[130],"impact":[140],"on":[141],"general":[143],"fluctuation-dissipation":[147],"theorem":[148],"derived":[149],"for":[150],"weak":[151],"forcing.":[153]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}