{"id":"https://openalex.org/W2054847121","doi":"https://doi.org/10.3390/e15093396","title":"Information Entropy As a Basic Building Block of Complexity Theory","display_name":"Information Entropy As a Basic Building Block of Complexity Theory","publication_year":2013,"publication_date":"2013-08-29","ids":{"openalex":"https://openalex.org/W2054847121","doi":"https://doi.org/10.3390/e15093396","mag":"2054847121"},"language":"en","primary_location":{"id":"doi:10.3390/e15093396","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e15093396","pdf_url":"https://www.mdpi.com/1099-4300/15/9/3396/pdf?version=1424785072","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/1099-4300/15/9/3396/pdf?version=1424785072","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052735725","display_name":"Jianbo Gao","orcid":"https://orcid.org/0000-0002-8832-5664"},"institutions":[{"id":"https://openalex.org/I150807315","display_name":"Guangxi University","ror":"https://ror.org/02c9qn167","country_code":"CN","type":"education","lineage":["https://openalex.org/I150807315"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jianbo Gao","raw_affiliation_strings":["PMB Intelligence LLC, Sunnyvale, CA 94087, USA","School of Mechanical Engineering and China-Asean Research Institute, Guangxi University,100 Daxue Road, Nanning 530005, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"PMB Intelligence LLC, Sunnyvale, CA 94087, USA","institution_ids":[]},{"raw_affiliation_string":"School of Mechanical Engineering and China-Asean Research Institute, Guangxi University,100 Daxue Road, Nanning 530005, China","institution_ids":["https://openalex.org/I150807315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082745291","display_name":"Feiyan Liu","orcid":"https://orcid.org/0000-0001-9435-9353"},"institutions":[{"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":"Feiyan Liu","raw_affiliation_strings":["Management School, University of Chinese Academy of Sciences, Beijing 100190, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Management School, University of Chinese Academy of Sciences, Beijing 100190, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030687054","display_name":"Jianfang Zhang","orcid":"https://orcid.org/0000-0002-3870-4906"},"institutions":[{"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":"Jianfang Zhang","raw_affiliation_strings":["Management School, University of Chinese Academy of Sciences, Beijing 100190, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Management School, University of Chinese Academy of Sciences, Beijing 100190, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100784386","display_name":"Jing Hu","orcid":null},"institutions":[{"id":"https://openalex.org/I150807315","display_name":"Guangxi University","ror":"https://ror.org/02c9qn167","country_code":"CN","type":"education","lineage":["https://openalex.org/I150807315"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jing Hu","raw_affiliation_strings":["PMB Intelligence LLC, Sunnyvale, CA 94087, USA","School of Mechanical Engineering and China-Asean Research Institute, Guangxi University,100 Daxue Road, Nanning 530005, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"PMB Intelligence LLC, Sunnyvale, CA 94087, USA","institution_ids":[]},{"raw_affiliation_string":"School of Mechanical Engineering and China-Asean Research Institute, Guangxi University,100 Daxue Road, Nanning 530005, China","institution_ids":["https://openalex.org/I150807315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050881210","display_name":"Yinping Cao","orcid":"https://orcid.org/0000-0003-3433-5397"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yinhe Cao","raw_affiliation_strings":["PMB Intelligence LLC, Sunnyvale, CA 94087, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"PMB Intelligence LLC, Sunnyvale, CA 94087, USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5052735725"],"corresponding_institution_ids":["https://openalex.org/I150807315"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":9.1214,"has_fulltext":true,"cited_by_count":64,"citation_normalized_percentile":{"value":0.97389465,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"15","issue":"9","first_page":"3396","last_page":"3418"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9866999983787537,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9866999983787537,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9783999919891357,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.9707000255584717,"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/information-diagram","display_name":"Information diagram","score":0.7864210605621338},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.6457728743553162},{"id":"https://openalex.org/keywords/information-theory","display_name":"Information theory","score":0.6156011819839478},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5550567507743835},{"id":"https://openalex.org/keywords/joint-entropy","display_name":"Joint entropy","score":0.5238249897956848},{"id":"https://openalex.org/keywords/joint-quantum-entropy","display_name":"Joint quantum entropy","score":0.49144279956817627},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48715731501579285},{"id":"https://openalex.org/keywords/maximum-entropy-thermodynamics","display_name":"Maximum entropy thermodynamics","score":0.4751179814338684},{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.4191117584705353},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.396618515253067},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37969303131103516},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.29935356974601746},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2542451024055481},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.22071179747581482},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1160016655921936},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10858634114265442},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10398948192596436}],"concepts":[{"id":"https://openalex.org/C67935508","wikidata":"https://www.wikidata.org/wiki/Q17078448","display_name":"Information diagram","level":5,"score":0.7864210605621338},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.6457728743553162},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.6156011819839478},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5550567507743835},{"id":"https://openalex.org/C106752470","wikidata":"https://www.wikidata.org/wiki/Q1364826","display_name":"Joint entropy","level":3,"score":0.5238249897956848},{"id":"https://openalex.org/C42047476","wikidata":"https://www.wikidata.org/wiki/Q6269544","display_name":"Joint quantum entropy","level":3,"score":0.49144279956817627},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48715731501579285},{"id":"https://openalex.org/C49775889","wikidata":"https://www.wikidata.org/wiki/Q6795896","display_name":"Maximum entropy thermodynamics","level":4,"score":0.4751179814338684},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.4191117584705353},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.396618515253067},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37969303131103516},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.29935356974601746},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2542451024055481},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.22071179747581482},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1160016655921936},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10858634114265442},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10398948192596436}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/e15093396","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e15093396","pdf_url":"https://www.mdpi.com/1099-4300/15/9/3396/pdf?version=1424785072","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:7877da60114e4f54b457fe7eba9639eb","is_oa":true,"landing_page_url":"https://doaj.org/article/7877da60114e4f54b457fe7eba9639eb","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 15, Iss 9, Pp 3396-3418 (2013)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/15/9/3396/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e15093396","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 15; Issue 9; Pages: 3396-3418","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e15093396","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e15093396","pdf_url":"https://www.mdpi.com/1099-4300/15/9/3396/pdf?version=1424785072","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/F4320321133","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2054847121.pdf","grobid_xml":"https://content.openalex.org/works/W2054847121.grobid-xml"},"referenced_works_count":95,"referenced_works":["https://openalex.org/W28106125","https://openalex.org/W44712423","https://openalex.org/W129002951","https://openalex.org/W564665047","https://openalex.org/W616447529","https://openalex.org/W1494137514","https://openalex.org/W1963744974","https://openalex.org/W1978909760","https://openalex.org/W1983874169","https://openalex.org/W1985554750","https://openalex.org/W1988374952","https://openalex.org/W1988557663","https://openalex.org/W1991486559","https://openalex.org/W1993470421","https://openalex.org/W1993933805","https://openalex.org/W1994836995","https://openalex.org/W1995875735","https://openalex.org/W1998018979","https://openalex.org/W1999706070","https://openalex.org/W2004022711","https://openalex.org/W2005097301","https://openalex.org/W2006688715","https://openalex.org/W2009387827","https://openalex.org/W2012703902","https://openalex.org/W2013138671","https://openalex.org/W2017994511","https://openalex.org/W2020524426","https://openalex.org/W2020829707","https://openalex.org/W2021760137","https://openalex.org/W2027278675","https://openalex.org/W2027825490","https://openalex.org/W2032121576","https://openalex.org/W2032610607","https://openalex.org/W2041905826","https://openalex.org/W2044437392","https://openalex.org/W2044984635","https://openalex.org/W2046364576","https://openalex.org/W2048866507","https://openalex.org/W2051270523","https://openalex.org/W2055084071","https://openalex.org/W2055739550","https://openalex.org/W2059421754","https://openalex.org/W2059851411","https://openalex.org/W2061574746","https://openalex.org/W2061863908","https://openalex.org/W2062411631","https://openalex.org/W2063025399","https://openalex.org/W2070631858","https://openalex.org/W2072224206","https://openalex.org/W2073630396","https://openalex.org/W2075387797","https://openalex.org/W2077770566","https://openalex.org/W2078188082","https://openalex.org/W2078206416","https://openalex.org/W2083378218","https://openalex.org/W2084466685","https://openalex.org/W2086038013","https://openalex.org/W2087171258","https://openalex.org/W2088270034","https://openalex.org/W2092119928","https://openalex.org/W2092444755","https://openalex.org/W2092811626","https://openalex.org/W2093020097","https://openalex.org/W2097124571","https://openalex.org/W2098589686","https://openalex.org/W2099111195","https://openalex.org/W2100693443","https://openalex.org/W2106375138","https://openalex.org/W2110816718","https://openalex.org/W2116966269","https://openalex.org/W2122962290","https://openalex.org/W2124871568","https://openalex.org/W2126479355","https://openalex.org/W2137478377","https://openalex.org/W2141835281","https://openalex.org/W2150312211","https://openalex.org/W2155084532","https://openalex.org/W2157942701","https://openalex.org/W2165161896","https://openalex.org/W2165175537","https://openalex.org/W2479877058","https://openalex.org/W2761540959","https://openalex.org/W2797078163","https://openalex.org/W2887654604","https://openalex.org/W2993383518","https://openalex.org/W3027014473","https://openalex.org/W3101092929","https://openalex.org/W4205727720","https://openalex.org/W4233497874","https://openalex.org/W4234406933","https://openalex.org/W4255721438","https://openalex.org/W4301267015","https://openalex.org/W6605247117","https://openalex.org/W6647349971","https://openalex.org/W6647836698"],"related_works":["https://openalex.org/W3114186922","https://openalex.org/W2141902522","https://openalex.org/W2154864208","https://openalex.org/W2356689936","https://openalex.org/W2139507220","https://openalex.org/W2306107824","https://openalex.org/W2083462338","https://openalex.org/W1545685255","https://openalex.org/W4252827860","https://openalex.org/W4293030281"],"abstract_inverted_index":{"What":[0,3],"is":[1],"information?":[2],"role":[4,42],"does":[5],"information":[6,11,31,36,44,61],"entropy":[7,37,45,62],"play":[8,64],"in":[9,15,46,59],"this":[10],"exploding":[12],"age,":[13],"especially":[14],"understanding":[16],"emergent":[17],"behaviors":[18],"of":[19,30,43],"complex":[20],"systems?":[21],"To":[22],"answer":[23],"these":[24],"questions,":[25],"we":[26],"discuss":[27],"the":[28,33,41],"origin":[29],"entropy,":[32,40],"difference":[34],"between":[35],"and":[38,52,55],"thermodynamic":[39],"complexity":[47],"theories,":[48],"including":[49],"chaos":[50],"theory":[51],"fractal":[53],"theory,":[54],"speculate":[56],"new":[57],"fields":[58],"which":[60],"may":[63],"important":[65],"roles.":[66]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-30T17:31:21.811387","created_date":"2016-06-24T00:00:00"}
