{"id":"https://openalex.org/W7213100044","doi":"https://doi.org/10.48550/arxiv.2609.12676","title":"Mass Dependence of Araki Relative Entropy through Modular Theory","display_name":"Mass Dependence of Araki Relative Entropy through Modular Theory","publication_year":2026,"publication_date":"2026-09-11","ids":{"openalex":"https://openalex.org/W7213100044","doi":"https://doi.org/10.48550/arxiv.2609.12676"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.12676","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12676","pdf_url":"https://arxiv.org/pdf/2609.12676","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.12676","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5131001797","display_name":"M. S. Guimaraes","orcid":"https://orcid.org/0000-0003-0057-148X","observed_orcids":["https://orcid.org/0000-0003-0057-148X"]},"institutions":[{"id":"https://openalex.org/I40034438","display_name":"Universidade do Estado do Rio de Janeiro","ror":"https://ror.org/0198v2949","country_code":"BR","type":"education","lineage":["https://openalex.org/I40034438"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Guimaraes, M. S.","raw_affiliation_strings":["UERJ -Universidade do Estado do Rio de Janeiro , Instituto de F\u00edsica , Departamento de F\u00edsica Te\u00f3rica , Rua S\u00e3o Francisco Xavier 524 , 20550-013 , Maracan\u00e3 , Rio de Janeiro , Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UERJ -Universidade do Estado do Rio de Janeiro , Instituto de F\u00edsica , Departamento de F\u00edsica Te\u00f3rica , Rua S\u00e3o Francisco Xavier 524 , 20550-013 , Maracan\u00e3 , Rio de Janeiro , Brazil","institution_ids":["https://openalex.org/I40034438"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001695910","display_name":"I. Roditi","orcid":"https://orcid.org/0000-0003-2363-5626","observed_orcids":["https://orcid.org/0000-0003-2363-5626"]},"institutions":[{"id":"https://openalex.org/I4210125245","display_name":"Centro Brasileiro de Pesquisas F\u00edsicas","ror":"https://ror.org/02wnmk332","country_code":"BR","type":"facility","lineage":["https://openalex.org/I4210125245","https://openalex.org/I4210151455"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Roditi, I.","raw_affiliation_strings":["CBPF -Centro Brasileiro de Pesquisas F\u00edsicas , Rua Dr. Xavier Sigaud 150 , 22290-180 , Rio de Janeiro , Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CBPF -Centro Brasileiro de Pesquisas F\u00edsicas , Rua Dr. Xavier Sigaud 150 , 22290-180 , Rio de Janeiro , Brazil","institution_ids":["https://openalex.org/I4210125245"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035082428","display_name":"S. P. Sorella","orcid":"https://orcid.org/0000-0002-6051-6960","observed_orcids":["https://orcid.org/0000-0002-6051-6960"]},"institutions":[{"id":"https://openalex.org/I40034438","display_name":"Universidade do Estado do Rio de Janeiro","ror":"https://ror.org/0198v2949","country_code":"BR","type":"education","lineage":["https://openalex.org/I40034438"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Sorella, S. P.","raw_affiliation_strings":["UERJ -Universidade do Estado do Rio de Janeiro , Instituto de F\u00edsica , Departamento de F\u00edsica Te\u00f3rica , Rua S\u00e3o Francisco Xavier 524 , 20550-013 , Maracan\u00e3 , Rio de Janeiro , Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UERJ -Universidade do Estado do Rio de Janeiro , Instituto de F\u00edsica , Departamento de F\u00edsica Te\u00f3rica , Rua S\u00e3o Francisco Xavier 524 , 20550-013 , Maracan\u00e3 , Rio de Janeiro , Brazil","institution_ids":["https://openalex.org/I40034438"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.9164999723434448,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.9164999723434448,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10025","display_name":"Black Holes and Theoretical Physics","score":0.016300000250339508,"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/T11804","display_name":"Quantum many-body systems","score":0.009700000286102295,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/modular-theory","display_name":"modular theory","score":0.7490000128746033},{"id":"https://openalex.org/keywords/mass-dependence","display_name":"mass dependence","score":0.7390000224113464},{"id":"https://openalex.org/keywords/scalar-field","display_name":"scalar field","score":0.5040000081062317},{"id":"https://openalex.org/keywords/modular-flow","display_name":"modular flow","score":0.6019999980926514},{"id":"https://openalex.org/keywords/spectral-representation","display_name":"spectral representation","score":0.44699999690055847},{"id":"https://openalex.org/keywords/transverse-mass","display_name":"transverse mass","score":0.5070000290870667}],"concepts":[{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.6141999959945679},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.5364000201225281},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5320000052452087},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.482699990272522},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4641000032424927},{"id":"https://openalex.org/C24495805","wikidata":"https://www.wikidata.org/wiki/Q7269091","display_name":"Quantum relative entropy","level":5,"score":0.4629000127315521},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4602999985218048},{"id":"https://openalex.org/C42047476","wikidata":"https://www.wikidata.org/wiki/Q6269544","display_name":"Joint quantum entropy","level":3,"score":0.4578000009059906},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.43050000071525574},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36910000443458557},{"id":"https://openalex.org/C118733216","wikidata":"https://www.wikidata.org/wiki/Q332504","display_name":"Absolute continuity","level":2,"score":0.3675999939441681},{"id":"https://openalex.org/C9136319","wikidata":"https://www.wikidata.org/wiki/Q362640","display_name":"Covariant transformation","level":2,"score":0.36329999566078186},{"id":"https://openalex.org/C54937798","wikidata":"https://www.wikidata.org/wiki/Q2024141","display_name":"Massless particle","level":2,"score":0.35760000348091125},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.35409998893737793},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.34439998865127563},{"id":"https://openalex.org/C5084201","wikidata":"https://www.wikidata.org/wiki/Q17090689","display_name":"Generalized relative entropy","level":5,"score":0.31540000438690186},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.31439998745918274},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.31349998712539673},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.31220000982284546},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.3109000027179718},{"id":"https://openalex.org/C130295795","wikidata":"https://www.wikidata.org/wiki/Q3550684","display_name":"Unitarity","level":2,"score":0.3098999857902527},{"id":"https://openalex.org/C2777925532","wikidata":"https://www.wikidata.org/wiki/Q5357201","display_name":"Mass gap","level":2,"score":0.30410000681877136},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30309998989105225},{"id":"https://openalex.org/C95857938","wikidata":"https://www.wikidata.org/wiki/Q658429","display_name":"Vector bundle","level":2,"score":0.3003999888896942},{"id":"https://openalex.org/C125252325","wikidata":"https://www.wikidata.org/wiki/Q1345213","display_name":"Entropy rate","level":4,"score":0.3001999855041504},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.2879999876022339},{"id":"https://openalex.org/C107706756","wikidata":"https://www.wikidata.org/wiki/Q219637","display_name":"Bessel function","level":2,"score":0.28600001335144043},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2847000062465668},{"id":"https://openalex.org/C107165499","wikidata":"https://www.wikidata.org/wiki/Q1366833","display_name":"Rapidity","level":3,"score":0.2825999855995178},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.2766999900341034},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.27309998869895935},{"id":"https://openalex.org/C35304006","wikidata":"https://www.wikidata.org/wiki/Q5962","display_name":"Boltzmann constant","level":2,"score":0.26969999074935913},{"id":"https://openalex.org/C101973423","wikidata":"https://www.wikidata.org/wiki/Q6961323","display_name":"Von Neumann entropy","level":4,"score":0.26820001006126404},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.2630000114440918},{"id":"https://openalex.org/C47422493","wikidata":"https://www.wikidata.org/wiki/Q2755127","display_name":"Wedge (geometry)","level":2,"score":0.2599000036716461},{"id":"https://openalex.org/C114852677","wikidata":"https://www.wikidata.org/wiki/Q899044","display_name":"Fock space","level":2,"score":0.25859999656677246},{"id":"https://openalex.org/C2777151079","wikidata":"https://www.wikidata.org/wiki/Q141160","display_name":"Parity (physics)","level":2,"score":0.2533999979496002}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.12676","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12676","pdf_url":"https://arxiv.org/pdf/2609.12676","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2609.12676","doi":"https://doi.org/10.48550/arxiv.2609.12676","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.12676","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.12676","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12676","pdf_url":"https://arxiv.org/pdf/2609.12676","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3836668482","display_name":null,"funder_award_id":"309793/2023-8","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G5268021672","display_name":null,"funder_award_id":"2024-7","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G7239851934","display_name":null,"funder_award_id":"302991/2024-7","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G7267620529","display_name":null,"funder_award_id":"309793/2023-8","funder_id":"https://openalex.org/F4320322749","funder_display_name":"Funda\u00e7\u00e3o Carlos Chagas Filho de Amparo \u00e0 Pesquisa do Estado do Rio de Janeiro"}],"funders":[{"id":"https://openalex.org/F4320321091","display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","ror":"https://ror.org/00x0ma614"},{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320322749","display_name":"Funda\u00e7\u00e3o Carlos Chagas Filho de Amparo \u00e0 Pesquisa do Estado do Rio de Janeiro","ror":"https://ror.org/03kk0s825"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213100044.pdf","grobid_xml":"https://content.openalex.org/works/W7213100044.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W2033879010","https://openalex.org/W2077034480","https://openalex.org/W2909316041","https://openalex.org/W2918878048","https://openalex.org/W2948925700","https://openalex.org/W3114381054","https://openalex.org/W4239588355","https://openalex.org/W4411987572","https://openalex.org/W4416074274","https://openalex.org/W4416771128"],"related_works":["https://openalex.org/W4416771128","https://openalex.org/W4407632340","https://openalex.org/W4416074274","https://openalex.org/W4411828812","https://openalex.org/W2918878048","https://openalex.org/W4408502475","https://openalex.org/W7212078817","https://openalex.org/W4320813916","https://openalex.org/W6920472560","https://openalex.org/W4388655154"],"abstract_inverted_index":{"Building":[0],"on":[1,23,69,83],"the":[2,7,24,27,37,42,46,65,126,134,138,195,208],"established":[3],"one-particle":[4,43],"formula":[5],"for":[6,93,149],"Araki":[8,154],"relative":[9,155],"entropy":[10,156,172],"of":[11,26,41,62,64],"coherent":[12],"states,":[13],"we":[14,101],"study":[15],"how":[16],"its":[17,153],"value":[18,193],"acquires":[19],"a":[20,31,59,87,110,118,180,191],"nontrivial":[21],"dependence":[22],"mass":[25,184],"scalar":[28],"field.":[29],"For":[30],"localized":[32],"vector":[33],"$h$":[34],"belonging":[35],"to":[36,56,147,190,204],"standard":[38,67],"subspace":[39,68],"$H_m$":[40],"Hilbert":[44],"space,":[45],"known":[47],"quadratic-form":[48],"expression":[49,72],"is:":[50],"$S_{H_m}(h)=-\\langle":[51],"h,\\log\u03b4_{H_m}\\,h\\rangle$.":[52],"Our":[53],"contribution":[54],"is":[55,73,157,173],"construct":[57],"explicitly":[58],"mass-indexed":[60],"family":[61,144],"vectors":[63],"wedge":[66],"which":[70],"this":[71],"evaluated.":[74],"The":[75,143,171,200],"mass-shell":[76],"map":[77],"$h_m=E_mf$":[78],"organizes":[79],"four":[80],"structural":[81],"conditions":[82],"rapidity":[84,105],"representatives---on-shell":[85],"dependence,":[86],"controlled":[88],"massless":[89],"boundary":[90,141],"value,":[91],"decay":[92],"large":[94,177],"real":[95],"rapidity,":[96],"and":[97,117,137,152,159,188],"Bisognano--Wichmann":[98,135],"strip":[99,136],"analyticity---and":[100],"exhibit":[102],"an":[103,163],"entire":[104],"wave":[106],"function,":[107],"built":[108],"from":[109],"doubled":[111],"light-cone":[112],"phase,":[113],"two":[114],"sinc":[115],"factors,":[116],"Gaussian":[119],"pair,":[120],"that":[121,167],"satisfies":[122],"them":[123],"together":[124],"with":[125,162],"sharp":[127],"localization":[128],"criterion:":[129],"Hardy-type":[130],"$L^2$":[131],"control":[132],"throughout":[133],"exact":[139,164],"Tomita":[140],"relation.":[142],"therefore":[145],"belongs":[146],"$H_m(\\W_R)$":[148],"every":[150],"$m>0$,":[151],"finite":[158,192],"strictly":[160],"positive,":[161],"spectral":[165],"representation":[166],"makes":[168],"positivity":[169],"manifest.":[170],"strongly":[174],"suppressed":[175],"at":[176,182],"mass,":[178],"attains":[179],"maximum":[181],"intermediate":[183],"in":[185],"$1+1$":[186],"dimension,":[187],"converges":[189],"along":[194],"modular":[196],"flow":[197],"as":[198],"$m\\to0^+$.":[199],"construction":[201],"extends":[202],"fiberwise":[203],"$1{+}d$":[205],"dimensions":[206],"through":[207],"transverse":[209],"mass.":[210]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-15T00:00:00"}
