{"id":"https://openalex.org/W7212905226","doi":"https://doi.org/10.48550/arxiv.2609.12068","title":"Thermodynamic Formalism Out of Equilibrium Part II: Semi-Ruelle Operator, Conformal Measures, and Effective Expansion and Quasi-Compactness","display_name":"Thermodynamic Formalism Out of Equilibrium Part II: Semi-Ruelle Operator, Conformal Measures, and Effective Expansion and Quasi-Compactness","publication_year":2026,"publication_date":"2026-09-10","ids":{"openalex":"https://openalex.org/W7212905226","doi":"https://doi.org/10.48550/arxiv.2609.12068"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.12068","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12068","pdf_url":"https://arxiv.org/pdf/2609.12068","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/2609.12068","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001543425","display_name":"Snir Ben Ovadia","orcid":"https://orcid.org/0009-0003-5799-6136","observed_orcids":["https://orcid.org/0009-0003-5799-6136"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ovadia, Snir Ben","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5001543425"],"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9990000128746033,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9990000128746033,"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/T13234","display_name":"p-Adic Analysis and Mathematical Physics","score":0.0003000000142492354,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.00019999999494757503,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/conformal-measures","display_name":"conformal measures","score":0.9929999709129333},{"id":"https://openalex.org/keywords/harmonic-functions","display_name":"harmonic functions","score":0.718999981880188},{"id":"https://openalex.org/keywords/topological-markov-shifts","display_name":"topological Markov shifts","score":0.8500000238418579},{"id":"https://openalex.org/keywords/quasi-compactness","display_name":"quasi-compactness","score":0.9309999942779541},{"id":"https://openalex.org/keywords/spectral-gap","display_name":"spectral gap","score":0.8059999942779541},{"id":"https://openalex.org/keywords/stationary-measures","display_name":"stationary measures","score":0.9459999799728394},{"id":"https://openalex.org/keywords/similarity-dimension","display_name":"similarity dimension","score":0.8100000023841858}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6675000190734863},{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.5892000198364258},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.4982999861240387},{"id":"https://openalex.org/C9259290","wikidata":"https://www.wikidata.org/wiki/Q745215","display_name":"Variational principle","level":2,"score":0.4797999858856201},{"id":"https://openalex.org/C627467","wikidata":"https://www.wikidata.org/wiki/Q599027","display_name":"Harmonic function","level":2,"score":0.44449999928474426},{"id":"https://openalex.org/C2778114796","wikidata":"https://www.wikidata.org/wiki/Q7575194","display_name":"Spectral gap","level":2,"score":0.4262999892234802},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.41519999504089355},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.3944000005722046},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.383899986743927},{"id":"https://openalex.org/C158444337","wikidata":"https://www.wikidata.org/wiki/Q2510435","display_name":"Gibbs measure","level":2,"score":0.3650999963283539},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.35920000076293945},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3569999933242798},{"id":"https://openalex.org/C2778999785","wikidata":"https://www.wikidata.org/wiki/Q5136697","display_name":"Cluster expansion","level":2,"score":0.3310999870300293},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.3294999897480011},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.328900009393692},{"id":"https://openalex.org/C41607394","wikidata":"https://www.wikidata.org/wiki/Q2420179","display_name":"Thermodynamic potential","level":2,"score":0.31709998846054077},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.31470000743865967},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.3084999918937683},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.3034999966621399},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.29600000381469727},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.29280000925064087},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.2833999991416931},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.2732999920845032},{"id":"https://openalex.org/C131157278","wikidata":"https://www.wikidata.org/wiki/Q51363","display_name":"Thermodynamic equilibrium","level":2,"score":0.27149999141693115},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.2700999975204468},{"id":"https://openalex.org/C24743483","wikidata":"https://www.wikidata.org/wiki/Q1154848","display_name":"Potential theory","level":2,"score":0.26899999380111694},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2632000148296356},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.262800008058548},{"id":"https://openalex.org/C42357961","wikidata":"https://www.wikidata.org/wiki/Q213363","display_name":"Open set","level":2,"score":0.2621000111103058},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.2583000063896179}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.12068","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12068","pdf_url":"https://arxiv.org/pdf/2609.12068","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.2609.12068","doi":"https://doi.org/10.48550/arxiv.2609.12068","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.12068","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:2609.12068","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12068","pdf_url":"https://arxiv.org/pdf/2609.12068","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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212905226.pdf","grobid_xml":"https://content.openalex.org/works/W7212905226.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W6910676767","https://openalex.org/W7162002874"],"related_works":["https://openalex.org/W7055266798","https://openalex.org/W2898022074","https://openalex.org/W2089020156","https://openalex.org/W4393929926","https://openalex.org/W7117876007","https://openalex.org/W4401407873","https://openalex.org/W4245093227","https://openalex.org/W4388787516","https://openalex.org/W4416095734","https://openalex.org/W3033009045"],"abstract_inverted_index":{"We":[0,47,58,69,75],"introduce":[1,48],"a":[2,16,29,33,44,71,77,172,180],"general":[3],"machinery":[4],"to":[5,80,143],"study":[6],"{\\em":[7,50,89,113,120,154,163],"thermodynamic":[8],"formalism":[9],"out":[10,91,115],"of":[11,15,92,116,153,187,195,200],"equilibrium}:":[12],"The":[13],"thermodynamics":[14],"topological":[17],"Markov":[18],"shift":[19],"(denoted":[20],"by":[21,28,43,137],"$\u03a3^-$)":[22],"where":[23,127],"the":[24,39,49,66,81,88,98,107,125,128,132,150,162,193],"potential":[25],"is":[26,41,95,135,167],"given":[27,136],"random":[30,129],"walk":[31,130],"on":[32,55,131,157,171,192],"compact":[34],"metric":[35],"space":[36],"$X$":[37,134],"(and":[38],"randomness":[40],"driven":[42],"Gibbs":[45],"process).":[46],"semi-Ruelle":[51,67,165],"operator},":[52],"which":[53,94],"acts":[54],"$C(\u03a3^-\\times":[56],"X)$.":[57],"construct":[59],"conformal":[60],"measures":[61,105],"and":[62,100,118,147,189],"harmonic":[63],"functions":[64],"for":[65,87],"operator.":[68],"present":[70],"few":[72],"applications:":[73],"(1)":[74],"provide":[76],"new":[78],"proof":[79],"POE":[82,108],"variational":[83,109],"principle":[84,110],"(POE":[85],"stands":[86],"pressure":[90],"equilibrium}":[93],"associated":[96],"with":[97],"process),":[99],"we":[101,159],"show":[102,160],"that":[103,161],"maximizing":[104],"in":[106,198],"admit":[111],"positive":[112],"entropy":[114],"equilibrium},":[117],"satisfy":[119],"semi-Gibbs":[121],"estimates}.":[122],"(2)":[123],"In":[124],"setting":[126],"fiber":[133],"$C^{1+}$":[138],"diffeomorphisms":[139],"(which":[140],"are":[141],"allowed":[142],"be":[144],"very":[145],"dissipative),":[146],"it":[148],"satisfies":[149],"open":[151],"condition":[152],"effective":[155],"expansion":[156],"average},":[158],"averaged":[164],"operator}":[166],"quasi-compact":[168],"when":[169,183],"acting":[170],"Sobolev":[173],"function":[174],"space.":[175],"An":[176],"application":[177],"includes":[178],"proving":[179,190],"spectral":[181],"gap":[182],"assuming":[184],"volume":[185],"decay":[186],"correlations,":[188],"bounds":[191],"dimension":[194],"stationary":[196],"measure":[197],"terms":[199],"similarity":[201],"dimension.":[202]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-15T00:00:00"}
