{"id":"https://openalex.org/W2335984944","doi":"https://doi.org/10.3390/e18090310","title":"SU(2) Yang\u2013Mills Theory: Waves, Particles, and Quantum Thermodynamics","display_name":"SU(2) Yang\u2013Mills Theory: Waves, Particles, and Quantum Thermodynamics","publication_year":2016,"publication_date":"2016-08-23","ids":{"openalex":"https://openalex.org/W2335984944","doi":"https://doi.org/10.3390/e18090310","mag":"2335984944"},"language":"en","primary_location":{"id":"doi:10.3390/e18090310","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e18090310","pdf_url":"https://www.mdpi.com/1099-4300/18/9/310/pdf?version=1471956974","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","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/18/9/310/pdf?version=1471956974","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009470263","display_name":"Ralf Hofmann","orcid":"https://orcid.org/0000-0001-6365-0631"},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]},{"id":"https://openalex.org/I223822909","display_name":"Heidelberg University","ror":"https://ror.org/038t36y30","country_code":"DE","type":"education","lineage":["https://openalex.org/I223822909"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Ralf Hofmann","raw_affiliation_strings":["Institut f\u00fcr Theoretische Physik, Universit\u00e4t Heidelberg, Philosophenweg 16, Heidelberg 69120, Germany","Institute for Photon Science and Synchrotron Radiation, Karlsruhe Institute of Technology, Eggenstein-Leopoldshafen 76344, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Theoretische Physik, Universit\u00e4t Heidelberg, Philosophenweg 16, Heidelberg 69120, Germany","institution_ids":["https://openalex.org/I223822909"]},{"raw_affiliation_string":"Institute for Photon Science and Synchrotron Radiation, Karlsruhe Institute of Technology, Eggenstein-Leopoldshafen 76344, Germany","institution_ids":["https://openalex.org/I102335020"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5009470263"],"corresponding_institution_ids":["https://openalex.org/I102335020","https://openalex.org/I223822909"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":1299,"currency":"EUR","value_usd":1400},"fwci":3.4663,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.93011493,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"18","issue":"9","first_page":"310","last_page":"310"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10224","display_name":"Quantum Chromodynamics and Particle Interactions","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy 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/T10224","display_name":"Quantum Chromodynamics and Particle Interactions","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy 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/T10048","display_name":"Particle physics theoretical and experimental studies","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy 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/T10527","display_name":"High-Energy Particle Collisions Research","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy 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/quantum-thermodynamics","display_name":"Quantum thermodynamics","score":0.5904028415679932},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.55662602186203},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.4674096405506134},{"id":"https://openalex.org/keywords/non-equilibrium-thermodynamics","display_name":"Non-equilibrium thermodynamics","score":0.46356117725372314},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.45454758405685425},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.39291563630104065},{"id":"https://openalex.org/keywords/theoretical-physics","display_name":"Theoretical physics","score":0.33749520778656006},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.3308870196342468}],"concepts":[{"id":"https://openalex.org/C2776897741","wikidata":"https://www.wikidata.org/wiki/Q12212546","display_name":"Quantum thermodynamics","level":3,"score":0.5904028415679932},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.55662602186203},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.4674096405506134},{"id":"https://openalex.org/C74859849","wikidata":"https://www.wikidata.org/wiki/Q2466686","display_name":"Non-equilibrium thermodynamics","level":2,"score":0.46356117725372314},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.45454758405685425},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.39291563630104065},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.33749520778656006},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3308870196342468}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3390/e18090310","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e18090310","pdf_url":"https://www.mdpi.com/1099-4300/18/9/310/pdf?version=1471956974","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:EVASTAR-Karlsruhe.de:1000059429","is_oa":false,"landing_page_url":"https://publikationen.bibliothek.kit.edu/1000059429","pdf_url":null,"source":{"id":"https://openalex.org/S4306401992","display_name":"Repository KITopen (Karlsruhe Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102335020","host_organization_name":"Karlsruhe Institute of Technology","host_organization_lineage":["https://openalex.org/I102335020"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy, 18 (9), 310","raw_type":"doc-type:article"},{"id":"pmh:oai:arXiv.org:1604.05136","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1604.05136","pdf_url":"https://arxiv.org/pdf/1604.05136","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:10f952f0066745b89bda378994c38659","is_oa":true,"landing_page_url":"https://doaj.org/article/10f952f0066745b89bda378994c38659","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 18, Iss 9, p 310 (2016)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/18/9/310/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e18090310","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 18; Issue 9; Pages: 310","raw_type":"Text"},{"id":"doi:10.5445/ir/1000059429","is_oa":true,"landing_page_url":"https://doi.org/10.5445/ir/1000059429","pdf_url":null,"source":{"id":"https://openalex.org/S7407052948","display_name":"KITopen","issn_l":null,"issn":[],"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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.3390/e18090310","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e18090310","pdf_url":"https://www.mdpi.com/1099-4300/18/9/310/pdf?version=1471956974","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":[{"display_name":"Affordable and clean energy","score":0.6100000143051147,"id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2335984944.pdf","grobid_xml":"https://content.openalex.org/works/W2335984944.grobid-xml"},"referenced_works_count":63,"referenced_works":["https://openalex.org/W1507400589","https://openalex.org/W1554821233","https://openalex.org/W1578434163","https://openalex.org/W1862698929","https://openalex.org/W1907701401","https://openalex.org/W1972008904","https://openalex.org/W1972281886","https://openalex.org/W1973787974","https://openalex.org/W1974659638","https://openalex.org/W1979483791","https://openalex.org/W1980001921","https://openalex.org/W1989067717","https://openalex.org/W1993902660","https://openalex.org/W2008480839","https://openalex.org/W2015302330","https://openalex.org/W2018666383","https://openalex.org/W2019179347","https://openalex.org/W2020356723","https://openalex.org/W2026827333","https://openalex.org/W2027710569","https://openalex.org/W2030311280","https://openalex.org/W2034224352","https://openalex.org/W2037941549","https://openalex.org/W2047539289","https://openalex.org/W2053805552","https://openalex.org/W2060036385","https://openalex.org/W2067137320","https://openalex.org/W2071939979","https://openalex.org/W2083941350","https://openalex.org/W2088424388","https://openalex.org/W2094512679","https://openalex.org/W2097772074","https://openalex.org/W2114062204","https://openalex.org/W2114870168","https://openalex.org/W2120889926","https://openalex.org/W2125707848","https://openalex.org/W2135934849","https://openalex.org/W2137410293","https://openalex.org/W2139937287","https://openalex.org/W2157489988","https://openalex.org/W2584039307","https://openalex.org/W2751881732","https://openalex.org/W2950887122","https://openalex.org/W3024256668","https://openalex.org/W3098831025","https://openalex.org/W3099914075","https://openalex.org/W3100626482","https://openalex.org/W3101229569","https://openalex.org/W3101599051","https://openalex.org/W3101877523","https://openalex.org/W3101968010","https://openalex.org/W3103989507","https://openalex.org/W3104352209","https://openalex.org/W3106493508","https://openalex.org/W3121956099","https://openalex.org/W3122378376","https://openalex.org/W3122695991","https://openalex.org/W3125874788","https://openalex.org/W4291432917","https://openalex.org/W4300438285","https://openalex.org/W4300513780","https://openalex.org/W4386783235","https://openalex.org/W6677130810"],"related_works":["https://openalex.org/W4296260748","https://openalex.org/W2313833598","https://openalex.org/W2766691699","https://openalex.org/W3155333635","https://openalex.org/W1885455437","https://openalex.org/W2081644498","https://openalex.org/W1650006545","https://openalex.org/W2796131162","https://openalex.org/W3098925485","https://openalex.org/W3040918329"],"abstract_inverted_index":{"We":[0,402],"elucidate":[1],"how":[2],"Quantum":[3],"Thermodynamics":[4],"at":[5,120,374],"temperature":[6,322],"T":[7],"emerges":[8],"from":[9,183],"pure":[10],"and":[11,59,85,203,228,243,272,315,362,371,379,422],"classical":[12,47],"S":[13,26,293,406,412],"U":[14,286,294,333,407,413],"(":[15,133,287,295,334,408,414],"2":[16,296,409,415],")":[17,289,297,336,410,416],"Yang\u2013Mills":[18,48],"theory":[19],"on":[20,341,404],"a":[21,35,52,82,98,150,168,180,187,254],"four-dimensional":[22],"Euclidean":[23],"spacetime":[24,123],"slice":[25],"1":[27,288,335],"\u00d7":[28,411],"R":[29],"3":[30],".":[31],"The":[32,139,221],"concept":[33],"of":[34,41,55,101,108,116,161,223,261,281,292,358,360,399,425],"(deconfining)":[36],"thermal":[37,67,103,163,325],"ground":[38,68,104],"state,":[39],"composed":[40],"certain":[42],"solutions":[43],"to":[44,193,257,320],"the":[45,66,71,102,162,217,258,266,279,285,342,385,429],"fundamental,":[46],"equation,":[49],"allows":[50],"for":[51,303,329],"unified":[53],"addressation":[54],"both":[56],"(classical)":[57],"wave-":[58,421],"(quantum)":[60],"particle-like":[61,423],"excitations":[62],"thereof.":[63],"More":[64],"definitely,":[65],"state":[69,105],"represents":[70],"interplay":[72],"between":[73],"nonpropagating,":[74],"periodic":[75],"configurations":[76],"which":[77,125,305,349],"are":[78,175,226,237,368],"electric-magnetically":[79],"(anti)selfdual":[80,230],"in":[81,106,143,284,324,377,381,397],"non-trivial":[83],"way":[84],"possess":[86],"topological":[87],"charge":[88],"modulus":[89],"unity.":[90],"Their":[91],"trivial-holonomy":[92],"versions\u2014Harrington\u2013Shepard":[93],"(HS)":[94],"(anti)calorons\u2014yield":[95],"an":[96,127,146,330,405],"accurate":[97],"priori":[99],"estimate":[100,165],"terms":[107,398],"spatially":[109],"coarse-grained":[110],"centers,":[111,340],"each":[112],"containing":[113],"one":[114],"quantum":[115],"action":[117],"\u210f":[118],"localized":[119],"its":[121],"inmost":[122],"point,":[124],"induce":[126],"inert":[128],"adjoint":[129],"scalar":[130],"field":[131,140],"\u03d5":[132,135,141,166,241],"|":[134,136,240,242],"spatio-temporally":[137],"constant).":[138],",":[142,153,167,277,298],"turn,":[144],"implies":[145],"effective":[147,393],"pure-gauge":[148],"configuration,":[149],"\u03bc":[151,169,275,316],"gs":[152,170,202,206,209,213],"accurately":[154],"describing":[155,420],"HS":[156,224,262,309,338],"(anti)caloron":[157,173,263,310,339],"overlap.":[158,252],"Spatial":[159],"homogeneity":[160],"ground-state":[164,198],"demands":[171],"that":[172],"centers":[174],"densely":[176],"packed,":[177],"thus":[178],"representing":[179],"collective":[181],"departure":[182],"(anti)selfduality.":[184],"Effectively,":[185],"such":[186,366],"\u201cnervous\u201d":[188],"microscopic":[189],"situation":[190],"gives":[191],"rise":[192],"two":[194],"static":[195,227],"phenomena:":[196],"finite":[197],"energy":[199,361],"density":[200,260],"\u03c1":[201,208],"pressure":[204],"P":[205,212],"with":[207,392],"=":[210],"\u2212":[211],"as":[214,216],"well":[215],"(adjoint)":[218],"Higgs":[219],"mechanism.":[220],"peripheries":[222],"(anti)calorons":[225],"resemble":[229],"dipole":[231,235],"fields":[232],"whose":[233],"apparent":[234],"moments":[236],"determined":[238],"by":[239,251,355],"T,":[244],"protecting":[245],"them":[246],"against":[247],"deformation":[248],"potentially":[249],"caused":[250],"Such":[253],"protection":[255],"extends":[256],"spatial":[259],"centers.":[264,311],"Thus":[265],"vacuum":[267],"electric":[268],"permittivity":[269],"\u03f5":[270,313],"0":[271,276,314,317],"magnetic":[273],"permeability":[274],"supporting":[278],"propagation":[280],"wave-like":[282,347],"disturbances":[283,304,427],"Cartan":[290],"subalgebra":[291],"can":[299],"be":[300,321],"reliably":[301],"calculated":[302],"do":[306],"not":[307],"probe":[308],"Both":[312],"turn":[318],"out":[319],"independent":[323],"equilibrium":[326],"but":[327],"also":[328],"isolated,":[331],"monochromatic":[332],"wave.":[337],"other":[343],"hand,":[344],"react":[345],"onto":[346],"disturbances,":[348],"would":[350],"resolve":[351],"their":[352],"spatio-temporal":[353],"structure,":[354],"indeterministic":[356],"emissions":[357],"quanta":[359],"momentum.":[363],"Thermodynamically":[364],"seen,":[365],"events":[367],"Boltzmann":[369],"weighted":[370],"occur":[372],"independently":[373],"distinct":[375],"locations":[376],"space":[378],"instants":[380],"(Minkowskian)":[382],"time,":[383],"entailing":[384],"Bose\u2013Einstein":[386],"distribution.":[387],"Small":[388],"correlative":[389],"ramifications":[390],"associate":[391],"radiative":[394],"corrections,":[395],"e.g.,":[396],"polarization":[400],"tensors.":[401],"comment":[403],"based":[417],"gauge-theory":[418],"model,":[419],"aspects":[424],"electromagnetic":[426],"within":[428],"so":[430],"far":[431],"experimentally/observationally":[432],"investigated":[433],"spectrum.":[434]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}