{"id":"https://openalex.org/W3166136349","doi":"https://doi.org/10.3390/e23080943","title":"The Matter of Time","display_name":"The Matter of Time","publication_year":2021,"publication_date":"2021-07-23","ids":{"openalex":"https://openalex.org/W3166136349","doi":"https://doi.org/10.3390/e23080943","mag":"3166136349","pmid":"https://pubmed.ncbi.nlm.nih.gov/34441083"},"language":"en","primary_location":{"id":"doi:10.3390/e23080943","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23080943","pdf_url":"https://www.mdpi.com/1099-4300/23/8/943/pdf","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/1099-4300/23/8/943/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022903177","display_name":"Arto Annila","orcid":"https://orcid.org/0000-0003-2955-2389"},"institutions":[{"id":"https://openalex.org/I133731052","display_name":"University of Helsinki","ror":"https://ror.org/040af2s02","country_code":"FI","type":"education","lineage":["https://openalex.org/I133731052"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Arto Annila","raw_affiliation_strings":["Department of Physics, University of Helsinki, 00014 Helsinki, Finland"],"affiliations":[{"raw_affiliation_string":"Department of Physics, University of Helsinki, 00014 Helsinki, Finland","institution_ids":["https://openalex.org/I133731052"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5022903177"],"corresponding_institution_ids":["https://openalex.org/I133731052"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":1460,"currency":"EUR","value_usd":1574},"fwci":1.65,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.83852796,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"23","issue":"8","first_page":"943","last_page":"943"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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":0.9829000234603882,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9793999791145325,"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/physics","display_name":"Physics","score":0.6270365715026855},{"id":"https://openalex.org/keywords/photon","display_name":"Photon","score":0.6153953075408936},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5865390300750732},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.5803104639053345},{"id":"https://openalex.org/keywords/energy-flow","display_name":"Energy flow","score":0.5444059371948242},{"id":"https://openalex.org/keywords/dynamical-billiards","display_name":"Dynamical billiards","score":0.47744494676589966},{"id":"https://openalex.org/keywords/energy-flux","display_name":"Energy flux","score":0.4690682590007782},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.4517766833305359},{"id":"https://openalex.org/keywords/time-evolution","display_name":"Time evolution","score":0.44334033131599426},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.44085171818733215},{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.42725762724876404},{"id":"https://openalex.org/keywords/theoretical-physics","display_name":"Theoretical physics","score":0.3526408076286316},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.33181291818618774},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.29372096061706543},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.20415031909942627},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16615787148475647}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6270365715026855},{"id":"https://openalex.org/C159317903","wikidata":"https://www.wikidata.org/wiki/Q3198","display_name":"Photon","level":2,"score":0.6153953075408936},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5865390300750732},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.5803104639053345},{"id":"https://openalex.org/C206815995","wikidata":"https://www.wikidata.org/wiki/Q1341307","display_name":"Energy flow","level":3,"score":0.5444059371948242},{"id":"https://openalex.org/C193605512","wikidata":"https://www.wikidata.org/wiki/Q2903467","display_name":"Dynamical billiards","level":2,"score":0.47744494676589966},{"id":"https://openalex.org/C55519028","wikidata":"https://www.wikidata.org/wiki/Q5377054","display_name":"Energy flux","level":2,"score":0.4690682590007782},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4517766833305359},{"id":"https://openalex.org/C106553664","wikidata":"https://www.wikidata.org/wiki/Q1156744","display_name":"Time evolution","level":2,"score":0.44334033131599426},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.44085171818733215},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.42725762724876404},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.3526408076286316},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.33181291818618774},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.29372096061706543},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.20415031909942627},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16615787148475647}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3390/e23080943","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23080943","pdf_url":"https://www.mdpi.com/1099-4300/23/8/943/pdf","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:34441083","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34441083","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:doaj.org/article:c8879e3555e74002b209e588138c642f","is_oa":true,"landing_page_url":"https://doaj.org/article/c8879e3555e74002b209e588138c642f","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 23, Iss 8, p 943 (2021)","raw_type":"article"},{"id":"pmh:oai:helda.helsinki.fi:10138/334176","is_oa":true,"landing_page_url":"http://hdl.handle.net/10138/334176","pdf_url":null,"source":{"id":"https://openalex.org/S4210213322","display_name":"Ty\u00f6v\u00e4entutkimus Vuosikirja","issn_l":"0784-1272","issn":["0784-1272","1459-7780"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:mdpi.com:/1099-4300/23/8/943/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e23080943","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 23; Issue 8; Pages: 943","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:8393911","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/8393911","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","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":"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/e23080943","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23080943","pdf_url":"https://www.mdpi.com/1099-4300/23/8/943/pdf","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":0.8700000047683716,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3166136349.pdf","grobid_xml":"https://content.openalex.org/works/W3166136349.grobid-xml"},"referenced_works_count":52,"referenced_works":["https://openalex.org/W242989516","https://openalex.org/W597974914","https://openalex.org/W607538787","https://openalex.org/W1562917170","https://openalex.org/W1598528911","https://openalex.org/W1660753265","https://openalex.org/W1910041862","https://openalex.org/W1962021760","https://openalex.org/W1967583334","https://openalex.org/W1976083037","https://openalex.org/W1980160396","https://openalex.org/W2000042664","https://openalex.org/W2012796346","https://openalex.org/W2019408728","https://openalex.org/W2029275475","https://openalex.org/W2049516912","https://openalex.org/W2058358280","https://openalex.org/W2063652693","https://openalex.org/W2087244225","https://openalex.org/W2101698406","https://openalex.org/W2102892532","https://openalex.org/W2107914009","https://openalex.org/W2108886591","https://openalex.org/W2134088714","https://openalex.org/W2140244209","https://openalex.org/W2146729985","https://openalex.org/W2155649614","https://openalex.org/W2156679433","https://openalex.org/W2489881823","https://openalex.org/W2622206762","https://openalex.org/W2794676372","https://openalex.org/W2799259903","https://openalex.org/W2894763192","https://openalex.org/W2950627632","https://openalex.org/W3023623741","https://openalex.org/W3034188108","https://openalex.org/W3100279372","https://openalex.org/W3103362336","https://openalex.org/W3103844541","https://openalex.org/W3162634547","https://openalex.org/W4212971612","https://openalex.org/W4231969216","https://openalex.org/W4234890892","https://openalex.org/W4246765045","https://openalex.org/W4251392365","https://openalex.org/W4301421397","https://openalex.org/W6676117097","https://openalex.org/W6680667558","https://openalex.org/W6681919610","https://openalex.org/W6682761565","https://openalex.org/W6785814052","https://openalex.org/W7048632861"],"related_works":["https://openalex.org/W4221163614","https://openalex.org/W3118433553","https://openalex.org/W4384470441","https://openalex.org/W3117131929","https://openalex.org/W2790862347","https://openalex.org/W4298328723","https://openalex.org/W3120590153","https://openalex.org/W3112240250","https://openalex.org/W2986536554","https://openalex.org/W2482793851"],"abstract_inverted_index":{"About":[0],"a":[1,38,44,53,138],"century":[2],"ago,":[3],"in":[4,33,72,109],"the":[5,10,16,23,29,73,91,98,103,116,134,158,163],"spirit":[6],"of":[7,12,26,36,40,46,59,76],"ancient":[8],"atomism,":[9],"quantum":[11],"light":[13],"was":[14],"renamed":[15],"photon":[17,30],"to":[18,67],"suggest":[19],"that":[20],"it":[21,121],"is":[22,122],"fundamental":[24],"element":[25],"everything.":[27],"Since":[28,90,151],"carries":[31],"energy":[32,70,155],"its":[34,161],"period":[35],"time,":[37],"flux":[39],"photons":[41],"inexorably":[42],"embodies":[43],"flow":[45,80],"time.":[47,77],"Thus,":[48,115,170],"time":[49,171],"comprises":[50,55],"periods":[51],"as":[52],"trek":[54],"legs.":[56],"The":[57,78],"flows":[58,92],"quanta":[60,164],"naturally":[61],"select":[62],"optimal":[63],"paths":[64],"(i.e.,":[65,105,111],"geodesics)":[66],"level":[68],"out":[69],"differences":[71,156],"least":[74],"amount":[75],"corresponding":[79],"equations":[81],"can":[82],"be":[83,88],"written,":[84],"but":[85,126,177],"they":[86],"cannot":[87],"solved.":[89],"affect":[93],"their":[94],"driving":[95],"forces,":[96],"affecting":[97],"flows,":[99],"and":[100,107,148,160,168],"so":[101],"on,":[102],"forces":[104,142],"causes)":[106],"changes":[108],"motions":[110],"consequences)":[112],"are":[113,145,153],"inseparable.":[114],"future":[117],"remains":[118],"unpredictable.":[119],"However,":[120],"not":[123,173],"all":[124],"arbitrary":[125],"rather":[127],"bounded":[128],"by":[129],"free":[130],"energy.":[131],"Eventually,":[132],"when":[133],"system":[135,159],"has":[136],"attained":[137],"stationary":[139],"state":[140],"where":[141],"tally,":[143],"there":[144,152],"no":[146,149,154],"causes":[147],"consequences.":[150],"between":[157],"surroundings,":[162],"only":[165],"orbit":[166],"on":[167],"on.":[169],"does":[172],"move":[174],"forward":[175],"either":[176],"circulates.":[178]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
