{"id":"https://openalex.org/W3033060561","doi":"https://doi.org/10.3390/e22080866","title":"Towards a Universal Measure of Complexity","display_name":"Towards a Universal Measure of Complexity","publication_year":2020,"publication_date":"2020-08-06","ids":{"openalex":"https://openalex.org/W3033060561","doi":"https://doi.org/10.3390/e22080866","mag":"3033060561","pmid":"https://pubmed.ncbi.nlm.nih.gov/33286637"},"language":"en","primary_location":{"id":"doi:10.3390/e22080866","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e22080866","pdf_url":"https://www.mdpi.com/1099-4300/22/8/866/pdf?version=1597227747","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":["arxiv","crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/22/8/866/pdf?version=1597227747","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Jaros\u0142aw Klamut","orcid":"https://orcid.org/0000-0002-5164-6931"},"institutions":[{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Jaros\u0142aw Klamut","raw_affiliation_strings":["Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland"],"raw_orcid":"https://orcid.org/0000-0002-5164-6931","affiliations":[{"raw_affiliation_string":"Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Ryszard Kutner","orcid":null},"institutions":[{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Ryszard Kutner","raw_affiliation_strings":["Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]}]},{"author_position":"last","author":{"id":null,"display_name":"Zbigniew R. Struzik","orcid":"https://orcid.org/0000-0002-1352-8897"},"institutions":[{"id":"https://openalex.org/I4210165842","display_name":"RIKEN Center for Advanced Photonics","ror":"https://ror.org/05vmjks78","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210110652","https://openalex.org/I4210165842"]},{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]},{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP","PL"],"is_corresponding":false,"raw_author_name":"Zbigniew R. Struzik","raw_affiliation_strings":["Advanced Center for Computing and Communication, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan","Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland","Graduate School of Education, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan"],"raw_orcid":"https://orcid.org/0000-0002-1352-8897","affiliations":[{"raw_affiliation_string":"Advanced Center for Computing and Communication, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan","institution_ids":["https://openalex.org/I4210165842"]},{"raw_affiliation_string":"Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]},{"raw_affiliation_string":"Graduate School of Education, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan","institution_ids":["https://openalex.org/I74801974"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4654613"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.1561,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.83276269,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"22","issue":"8","first_page":"866","last_page":"866"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12469","display_name":"Chaos, Complexity, and Education","score":0.32120001316070557,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12469","display_name":"Chaos, Complexity, and Education","score":0.32120001316070557,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.07970000058412552,"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/T14299","display_name":"Complex Systems and Dynamics","score":0.061400000005960464,"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/measure","display_name":"Measure (data warehouse)","score":0.6844000220298767},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5928999781608582},{"id":"https://openalex.org/keywords/complex-system","display_name":"Complex system","score":0.42480000853538513},{"id":"https://openalex.org/keywords/degrees-of-freedom","display_name":"Degrees of freedom (physics and chemistry)","score":0.41269999742507935},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.37059998512268066},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.3659000098705292}],"concepts":[{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.6844000220298767},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5928999781608582},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5925999879837036},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.42480000853538513},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.41269999742507935},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.38420000672340393},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.37059998512268066},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.3659000098705292},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.3294999897480011},{"id":"https://openalex.org/C2780598303","wikidata":"https://www.wikidata.org/wiki/Q65921492","display_name":"Flexibility (engineering)","level":2,"score":0.3269999921321869},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3165999948978424},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.3046000003814697},{"id":"https://openalex.org/C6435147","wikidata":"https://www.wikidata.org/wiki/Q5156627","display_name":"Complexity index","level":3,"score":0.30230000615119934},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.3000999987125397},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.29660001397132874},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2759000062942505},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25429999828338623}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3390/e22080866","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e22080866","pdf_url":"https://www.mdpi.com/1099-4300/22/8/866/pdf?version=1597227747","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:33286637","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33286637","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:arXiv.org:2006.01900","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2006.01900","pdf_url":"https://arxiv.org/pdf/2006.01900","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:d75547719ce14d1fba9596c33eb56945","is_oa":true,"landing_page_url":"https://doaj.org/article/d75547719ce14d1fba9596c33eb56945","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 22, Iss 8, p 866 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/22/8/866/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e22080866","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 22; Issue 8; Pages: 866","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7517468","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7517468","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/e22080866","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e22080866","pdf_url":"https://www.mdpi.com/1099-4300/22/8/866/pdf?version=1597227747","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":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320323873","display_name":"Uniwersytet Warszawski","ror":"https://ror.org/039bjqg32"},{"id":"https://openalex.org/F4320335039","display_name":"Narodowe Centrum Bada\u0144 i Rozwoju","ror":"https://ror.org/05pwfyy15"},{"id":"https://openalex.org/F4320338080","display_name":"European Social Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3033060561.pdf","grobid_xml":"https://content.openalex.org/works/W3033060561.grobid-xml"},"referenced_works_count":49,"referenced_works":["https://openalex.org/W26634739","https://openalex.org/W217881882","https://openalex.org/W317608397","https://openalex.org/W595863337","https://openalex.org/W1486182996","https://openalex.org/W1556573274","https://openalex.org/W1862394037","https://openalex.org/W1964677252","https://openalex.org/W1971658288","https://openalex.org/W1980977025","https://openalex.org/W1983874169","https://openalex.org/W1992015378","https://openalex.org/W1998982154","https://openalex.org/W2036613247","https://openalex.org/W2044203091","https://openalex.org/W2046945477","https://openalex.org/W2053047297","https://openalex.org/W2055281720","https://openalex.org/W2056651346","https://openalex.org/W2070051876","https://openalex.org/W2075606380","https://openalex.org/W2077204677","https://openalex.org/W2077949668","https://openalex.org/W2093802314","https://openalex.org/W2124637492","https://openalex.org/W2128590107","https://openalex.org/W2152331460","https://openalex.org/W2154383061","https://openalex.org/W2309298013","https://openalex.org/W2313034363","https://openalex.org/W2560743925","https://openalex.org/W2573484504","https://openalex.org/W2897257437","https://openalex.org/W2901930902","https://openalex.org/W3011959288","https://openalex.org/W3016689283","https://openalex.org/W3022585649","https://openalex.org/W3034145009","https://openalex.org/W3122938238","https://openalex.org/W4214495506","https://openalex.org/W4236361506","https://openalex.org/W4238910361","https://openalex.org/W4248636106","https://openalex.org/W4252222018","https://openalex.org/W4255142739","https://openalex.org/W6632920022","https://openalex.org/W6684996598","https://openalex.org/W6770238113","https://openalex.org/W6820856607"],"related_works":[],"abstract_inverted_index":{"Recently,":[0],"it":[1],"has":[2],"been":[3],"argued":[4],"that":[5,43,92],"entropy":[6,19],"can":[7],"be":[8],"a":[9,38,59,119,132,135],"direct":[10],"measure":[11,40,53,154],"of":[12,18,41,49,54,62,81,84,102,106,116,118,127,138,140,151,170],"complexity,":[13,23],"where":[14,65],"the":[15,66,70,74,79,82,93,97,107,114,128,168,178],"smaller":[16],"value":[17,27],"indicates":[20,28],"lower":[21],"system":[22,30,67,83,121,130,171],"while":[24],"its":[25,159,162],"larger":[26],"higher":[29],"complexity.":[31,50,88,180],"We":[32,89],"dispute":[33],"this":[34,146,152],"view":[35,48],"and":[36,110,134,174],"propose":[37],"universal":[39,52,153],"complexity":[42,55,72],"is":[44,56,73,96,142],"based":[45,57],"on":[46,58],"Gell-Mann's":[47],"Our":[51],"non-linear":[60],"transformation":[61],"time-dependent":[63],"entropy,":[64],"state":[68,100],"with":[69,131],"highest":[71],"most":[75,94,108,111],"distant":[76],"from":[77],"all":[78],"states":[80,117],"lesser":[85],"or":[86],"no":[87],"have":[90],"shown":[91,143],"complex":[95],"optimally":[98],"mixed":[99],"consisting":[101],"pure":[103],"states,":[104],"i.e.,":[105],"regular":[109],"disordered":[112],"which":[113],"space":[115],"given":[120],"allows.":[122],"A":[123],"parsimonious":[124],"paradigmatic":[125],"example":[126],"simplest":[129],"small":[133],"large":[136],"number":[137],"degrees":[139],"freedom":[141],"to":[144,164,167,176],"support":[145],"methodology.":[147],"Several":[148],"important":[149],"features":[150],"are":[155],"pointed":[156],"out,":[157],"especially":[158],"flexibility":[160],"(i.e.,":[161],"openness":[163],"extensions),":[165],"suitability":[166,175],"analysis":[169],"critical":[172],"behaviour,":[173],"study":[177],"dynamic":[179]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2020-06-12T00:00:00"}
