{"id":"https://openalex.org/W3154625306","doi":"https://doi.org/10.3390/sym13040721","title":"Multiscale Thermodynamics: Energy, Entropy, and Symmetry from Atoms to Bulk Behavior","display_name":"Multiscale Thermodynamics: Energy, Entropy, and Symmetry from Atoms to Bulk Behavior","publication_year":2021,"publication_date":"2021-04-19","ids":{"openalex":"https://openalex.org/W3154625306","doi":"https://doi.org/10.3390/sym13040721","mag":"3154625306"},"language":"en","primary_location":{"id":"doi:10.3390/sym13040721","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13040721","pdf_url":"https://www.mdpi.com/2073-8994/13/4/721/pdf?version=1618999893","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"preprint","indexed_in":["crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/13/4/721/pdf?version=1618999893","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002701748","display_name":"Ralph V. Chamberlin","orcid":"https://orcid.org/0000-0003-4187-4604"},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ralph Chamberlin","raw_affiliation_strings":["Department of Physics, Arizona State University, Tempe, AZ 85287-1504, USA","Arizona State University**"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Arizona State University, Tempe, AZ 85287-1504, USA","institution_ids":["https://openalex.org/I55732556"]},{"raw_affiliation_string":"Arizona State University**","institution_ids":["https://openalex.org/I55732556"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102707168","display_name":"Michael R. Clark","orcid":"https://orcid.org/0000-0003-1817-1548"},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael Clark","raw_affiliation_strings":["Department of Physics, Arizona State University, Tempe, AZ 85287-1504, USA","Arizona State University**"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Arizona State University, Tempe, AZ 85287-1504, USA","institution_ids":["https://openalex.org/I55732556"]},{"raw_affiliation_string":"Arizona State University**","institution_ids":["https://openalex.org/I55732556"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024563016","display_name":"Vladimiro M\u00fajica","orcid":"https://orcid.org/0000-0002-5237-4851"},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vladimiro Mujica","raw_affiliation_strings":["School of Molecular Science, Arizona State University, Tempe, AZ 85287-1604, USA","Arizona State University**"],"raw_orcid":"https://orcid.org/0000-0002-5237-4851","affiliations":[{"raw_affiliation_string":"School of Molecular Science, Arizona State University, Tempe, AZ 85287-1604, USA","institution_ids":["https://openalex.org/I55732556"]},{"raw_affiliation_string":"Arizona State University**","institution_ids":["https://openalex.org/I55732556"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103526226","display_name":"George H. Wolf","orcid":null},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"George Wolf","raw_affiliation_strings":["School of Molecular Science, Arizona State University, Tempe, AZ 85287-1604, USA","Arizona State University**"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Molecular Science, Arizona State University, Tempe, AZ 85287-1604, USA","institution_ids":["https://openalex.org/I55732556"]},{"raw_affiliation_string":"Arizona State University**","institution_ids":["https://openalex.org/I55732556"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5002701748"],"corresponding_institution_ids":["https://openalex.org/I55732556"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06191594,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"4","first_page":"721","last_page":"721"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":1.0,"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":1.0,"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/T11804","display_name":"Quantum many-body systems","score":0.9957000017166138,"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/T10581","display_name":"Neural dynamics and brain function","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/canonical-ensemble","display_name":"Canonical ensemble","score":0.7526098489761353},{"id":"https://openalex.org/keywords/microcanonical-ensemble","display_name":"Microcanonical ensemble","score":0.7226923704147339},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.703525960445404},{"id":"https://openalex.org/keywords/ising-model","display_name":"Ising model","score":0.6108094453811646},{"id":"https://openalex.org/keywords/spins","display_name":"Spins","score":0.5985395312309265},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.585811972618103},{"id":"https://openalex.org/keywords/statistical-ensemble","display_name":"Statistical ensemble","score":0.5592268109321594},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5416626334190369},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.539583146572113},{"id":"https://openalex.org/keywords/grand-canonical-ensemble","display_name":"Grand canonical ensemble","score":0.5157046914100647},{"id":"https://openalex.org/keywords/quantum-decoherence","display_name":"Quantum decoherence","score":0.4500822424888611},{"id":"https://openalex.org/keywords/ideal-gas","display_name":"Ideal gas","score":0.4206075072288513},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.3462042808532715},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.1204821765422821},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.11565932631492615},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.11242049932479858}],"concepts":[{"id":"https://openalex.org/C28556851","wikidata":"https://www.wikidata.org/wiki/Q1077753","display_name":"Canonical ensemble","level":3,"score":0.7526098489761353},{"id":"https://openalex.org/C101683677","wikidata":"https://www.wikidata.org/wiki/Q1077769","display_name":"Microcanonical ensemble","level":4,"score":0.7226923704147339},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.703525960445404},{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.6108094453811646},{"id":"https://openalex.org/C2778870898","wikidata":"https://www.wikidata.org/wiki/Q7577658","display_name":"Spins","level":2,"score":0.5985395312309265},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.585811972618103},{"id":"https://openalex.org/C50311922","wikidata":"https://www.wikidata.org/wiki/Q898535","display_name":"Statistical ensemble","level":4,"score":0.5592268109321594},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5416626334190369},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.539583146572113},{"id":"https://openalex.org/C29235156","wikidata":"https://www.wikidata.org/wiki/Q1153553","display_name":"Grand canonical ensemble","level":3,"score":0.5157046914100647},{"id":"https://openalex.org/C122527463","wikidata":"https://www.wikidata.org/wiki/Q578430","display_name":"Quantum decoherence","level":3,"score":0.4500822424888611},{"id":"https://openalex.org/C30342001","wikidata":"https://www.wikidata.org/wiki/Q172280","display_name":"Ideal gas","level":2,"score":0.4206075072288513},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3462042808532715},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.1204821765422821},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.11565932631492615},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.11242049932479858},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/sym13040721","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13040721","pdf_url":"https://www.mdpi.com/2073-8994/13/4/721/pdf?version=1618999893","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"mag:3154625306","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2104.06965.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:doaj.org/article:836b331b005145c79aa743d40ca5eb91","is_oa":true,"landing_page_url":"https://doaj.org/article/836b331b005145c79aa743d40ca5eb91","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":"Symmetry, Vol 13, Iss 4, p 721 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/4/721/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13040721","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":"Symmetry","raw_type":"Text"},{"id":"doi:10.48550/arxiv.2104.06965","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2104.06965","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.3390/sym13040721","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13040721","pdf_url":"https://www.mdpi.com/2073-8994/13/4/721/pdf?version=1618999893","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3154625306.pdf","grobid_xml":"https://content.openalex.org/works/W3154625306.grobid-xml"},"referenced_works_count":85,"referenced_works":["https://openalex.org/W126362881","https://openalex.org/W823494218","https://openalex.org/W1251834161","https://openalex.org/W1517374528","https://openalex.org/W1525565205","https://openalex.org/W1897509654","https://openalex.org/W1966315857","https://openalex.org/W1968532084","https://openalex.org/W1970383435","https://openalex.org/W1972030313","https://openalex.org/W1972197313","https://openalex.org/W1979111488","https://openalex.org/W1979550388","https://openalex.org/W1980416711","https://openalex.org/W1981822168","https://openalex.org/W1981869633","https://openalex.org/W1982789149","https://openalex.org/W1987047812","https://openalex.org/W1988388205","https://openalex.org/W1990090727","https://openalex.org/W1993826366","https://openalex.org/W1995883194","https://openalex.org/W2012422733","https://openalex.org/W2013542617","https://openalex.org/W2014504423","https://openalex.org/W2018224213","https://openalex.org/W2020210807","https://openalex.org/W2021820673","https://openalex.org/W2024162830","https://openalex.org/W2024221348","https://openalex.org/W2030669601","https://openalex.org/W2031487213","https://openalex.org/W2038246301","https://openalex.org/W2046061084","https://openalex.org/W2046567280","https://openalex.org/W2047616041","https://openalex.org/W2049905727","https://openalex.org/W2050915474","https://openalex.org/W2053047297","https://openalex.org/W2054335718","https://openalex.org/W2055281720","https://openalex.org/W2056080528","https://openalex.org/W2065502108","https://openalex.org/W2068674173","https://openalex.org/W2071470060","https://openalex.org/W2079540121","https://openalex.org/W2080911709","https://openalex.org/W2081357233","https://openalex.org/W2085311292","https://openalex.org/W2088141383","https://openalex.org/W2091350313","https://openalex.org/W2093337238","https://openalex.org/W2095938967","https://openalex.org/W2102277728","https://openalex.org/W2108947461","https://openalex.org/W2109171391","https://openalex.org/W2128220160","https://openalex.org/W2128706048","https://openalex.org/W2137971290","https://openalex.org/W2147078753","https://openalex.org/W2149801992","https://openalex.org/W2170797104","https://openalex.org/W2197820338","https://openalex.org/W2208271338","https://openalex.org/W2249735528","https://openalex.org/W2279534621","https://openalex.org/W2295788785","https://openalex.org/W2313418854","https://openalex.org/W2318093595","https://openalex.org/W2591651836","https://openalex.org/W2593970276","https://openalex.org/W2763785647","https://openalex.org/W2805143944","https://openalex.org/W2808871717","https://openalex.org/W2809540821","https://openalex.org/W2884062455","https://openalex.org/W2898471460","https://openalex.org/W2930574801","https://openalex.org/W3004320394","https://openalex.org/W3080397666","https://openalex.org/W3102603521","https://openalex.org/W3105946523","https://openalex.org/W3194584304","https://openalex.org/W4255208716","https://openalex.org/W6641615315"],"related_works":["https://openalex.org/W3044200205","https://openalex.org/W1980416711","https://openalex.org/W3099578856","https://openalex.org/W3104006204","https://openalex.org/W2072881373","https://openalex.org/W2580805239","https://openalex.org/W3103069854","https://openalex.org/W3098966159","https://openalex.org/W2186825102","https://openalex.org/W2142989872","https://openalex.org/W1501501128","https://openalex.org/W2527058785","https://openalex.org/W2551215896","https://openalex.org/W3037049177","https://openalex.org/W3101772483","https://openalex.org/W2784685070","https://openalex.org/W2036120844","https://openalex.org/W2189992120","https://openalex.org/W3105055622","https://openalex.org/W2622507957"],"abstract_inverted_index":{"Here,":[0],"we":[1,238],"investigate":[2,83],"how":[3,84],"the":[4,15,18,23,30,36,104,162,191,233,236,242,250,258,266,273,298,305,330],"local":[5],"properties":[6,244],"of":[7,17,26,38,61,70,93,115,120,122,127,187,194,245,269,300,307],"particles":[8,169,209],"in":[9,139,149,178,228,241,249,257,335],"a":[10,67,85,112,176,197,246,254,290],"thermal":[11,267,332],"bath":[12],"may":[13,88,211,264],"influence":[14],"thermodynamics":[16],"bath,":[19],"and":[20,65,172,253,272,322],"consequently":[21],"alter":[22,265],"statistical":[24],"mechanics":[25,180],"subsystems":[27],"that":[28,48,66,136,210,288],"comprise":[29],"bath.":[31,77],"We":[32,78],"are":[33,219,225],"guided":[34],"by":[35,55,155,175,303],"theory":[37],"small-system":[39],"thermodynamics,":[40],"which":[41,224,296],"is":[42,276],"based":[43,220],"on":[44,221,232,310],"two":[45],"primary":[46],"postulates:":[47],"small":[49,63,71,188],"systems":[50,72],"can":[51],"be":[52,153,212],"treated":[53],"self-consistently":[54],"coupling":[56],"them":[57],"to":[58,82,152,293,329],"an":[59,91,118],"ensemble":[60,69,92,119,252,275],"similarly":[62],"systems,":[64],"large":[68,86,113,185],"forms":[73],"its":[74],"own":[75],"thermodynamic":[76],"adapt":[79],"this":[80],"\u201cnanothermodynamics\u201d":[81],"system":[87,114],"subdivide":[89],"into":[90,117],"smaller":[94],"subsystems,":[95],"causing":[96],"internal":[97],"heterogeneity":[98],"across":[99],"multiple":[100],"size":[101],"scales.":[102],"For":[103],"semi-classical":[105,198],"ideal":[106,199],"gas,":[107,200],"maximum":[108],"entropy":[109,193],"favors":[110],"subdividing":[111],"\u201catoms\u201d":[116],"\u201cregions\u201d":[121],"variable":[123],"size.":[124],"The":[125],"mechanism":[126],"region":[128,141],"formation":[129],"could":[130],"come":[131],"from":[132],"quantum":[133,179,206],"exchange":[134,309],"symmetry":[135,207],"makes":[137],"atoms":[138,148],"each":[140],"indistinguishable,":[142,171],"while":[143],"decoherence":[144],"between":[145,235],"regions":[146,151,160,189],"allows":[147],"separate":[150],"distinguishable":[154,168],"their":[156],"distinct":[157],"locations.":[158],"Combining":[159,184],"reduces":[161],"total":[163],"entropy,":[164],"as":[165,173],"expected":[166],"when":[167],"become":[170],"required":[174],"theorem":[177],"for":[181,196,208,278],"sub-additive":[182],"entropy.":[183],"volumes":[186],"gives":[190],"usual":[192],"mixing":[195],"resolving":[201],"Gibbs":[202],"paradox":[203],"without":[204],"invoking":[205],"meters":[213],"apart.":[214],"Other":[215],"models":[216],"presented":[217],"here":[218],"Ising-like":[222,284],"spins,":[223,237],"solved":[226],"analytically":[227],"one":[229],"dimension.":[230],"Focusing":[231],"bonds":[234],"find":[239],"similarity":[240],"equilibrium":[243,331],"two-state":[247],"model":[248,256],"nanocanonical":[251],"three-state":[255],"canonical":[259],"ensemble.":[260],"Thus,":[261],"emergent":[262],"phenomena":[263],"behavior":[268],"microscopic":[270],"models,":[271],"correct":[274],"necessary":[277],"fully-accurate":[279],"predictions.":[280],"Another":[281],"result":[282],"using":[283],"spins":[285],"involves":[286],"simulations":[287,314],"include":[289],"nonlinear":[291],"correction":[292],"Boltzmann\u2019s":[294],"factor,":[295],"mimics":[297],"statistics":[299],"indistinguishable":[301],"states":[302],"imitating":[304],"dynamics":[306],"spin":[308],"intermediate":[311],"lengths.":[312],"These":[313],"exhibit":[315],"1/f-like":[316],"noise":[317,324],"at":[318,325],"low":[319],"frequencies":[320],"(f),":[321],"white":[323],"higher":[326],"f,":[327],"similar":[328],"fluctuations":[333],"found":[334],"many":[336],"materials.":[337]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}