{"id":"https://openalex.org/W7204903213","doi":"https://doi.org/10.48550/arxiv.2608.30871","title":"On the relaxation problem in statistical mechanics","display_name":"On the relaxation problem in statistical mechanics","publication_year":2026,"publication_date":"2026-08-31","ids":{"openalex":"https://openalex.org/W7204903213","doi":"https://doi.org/10.48550/arxiv.2608.30871"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.30871","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30871","pdf_url":"https://arxiv.org/pdf/2608.30871","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/2608.30871","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084119517","display_name":"Giuseppe Del Vecchio Del Vecchio","orcid":"https://orcid.org/0000-0001-7617-4937","observed_orcids":["https://orcid.org/0000-0001-7617-4937"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Del Vecchio, Giuseppe Del Vecchio","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5084119517"],"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.8535000085830688,"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":0.8535000085830688,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.11789999902248383,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.00860000029206276,"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/relaxation-problem","display_name":"relaxation problem","score":0.9179999828338623},{"id":"https://openalex.org/keywords/prediction","display_name":"prediction","score":0.5609999895095825},{"id":"https://openalex.org/keywords/irreversible-relaxation","display_name":"irreversible relaxation","score":0.6000000238418579},{"id":"https://openalex.org/keywords/loss-functions","display_name":"loss functions","score":0.7080000042915344},{"id":"https://openalex.org/keywords/out-of-sample-forecasting","display_name":"out-of-sample forecasting","score":0.6380000114440918},{"id":"https://openalex.org/keywords/initial-conditions","display_name":"initial conditions","score":0.3659999966621399}],"concepts":[{"id":"https://openalex.org/C99874945","wikidata":"https://www.wikidata.org/wiki/Q188715","display_name":"Statistical mechanics","level":2,"score":0.6798999905586243},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5788999795913696},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5683000087738037},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.49480000138282776},{"id":"https://openalex.org/C2780704645","wikidata":"https://www.wikidata.org/wiki/Q9251458","display_name":"Observer (physics)","level":2,"score":0.46369999647140503},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.45089998841285706},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.44119998812675476},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.387800008058548},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.35600000619888306},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.35280001163482666},{"id":"https://openalex.org/C53533937","wikidata":"https://www.wikidata.org/wiki/Q185020","display_name":"Histogram","level":3,"score":0.33649998903274536},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32030001282691956},{"id":"https://openalex.org/C116672817","wikidata":"https://www.wikidata.org/wiki/Q1454986","display_name":"Physical system","level":2,"score":0.3197000026702881},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.3156999945640564},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.31520000100135803},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.3147999942302704},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3068000078201294},{"id":"https://openalex.org/C48057537","wikidata":"https://www.wikidata.org/wiki/Q3551145","display_name":"Statistical theory","level":2,"score":0.302700012922287},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.3025999963283539},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.3000999987125397},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.2881999909877777},{"id":"https://openalex.org/C109546454","wikidata":"https://www.wikidata.org/wiki/Q3798604","display_name":"Information geometry","level":4,"score":0.2831999957561493},{"id":"https://openalex.org/C179434709","wikidata":"https://www.wikidata.org/wiki/Q899853","display_name":"H-theorem","level":5,"score":0.2786000072956085},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.27399998903274536},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.26499998569488525},{"id":"https://openalex.org/C2777855551","wikidata":"https://www.wikidata.org/wiki/Q12310021","display_name":"Subject (documents)","level":2,"score":0.2648000121116638},{"id":"https://openalex.org/C152139883","wikidata":"https://www.wikidata.org/wiki/Q252973","display_name":"Mutual information","level":2,"score":0.2621000111103058},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.25679999589920044}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.30871","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30871","pdf_url":"https://arxiv.org/pdf/2608.30871","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.30871","doi":"https://doi.org/10.48550/arxiv.2608.30871","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.30871","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.30871","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30871","pdf_url":"https://arxiv.org/pdf/2608.30871","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/G2037112959","display_name":"Extreme dynamics in interacting particle systems","funder_award_id":"ANR-23-CE30-0020","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G5020422105","display_name":null,"funder_award_id":"ANR-23-CE30","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7080048889","display_name":null,"funder_award_id":"ANR-23","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204903213.pdf","grobid_xml":"https://content.openalex.org/works/W7204903213.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W643674336","https://openalex.org/W3204186547","https://openalex.org/W2044232635","https://openalex.org/W2016782947","https://openalex.org/W2051479569","https://openalex.org/W2030455529","https://openalex.org/W2133600649","https://openalex.org/W2602465737","https://openalex.org/W4300587323","https://openalex.org/W3004404009"],"abstract_inverted_index":{"We":[0],"reformulate":[1],"the":[2,13,19,24,34,72,104,116,130,133,137,150],"relaxation":[3,91],"problem":[4],"in":[5,142],"statistical":[6],"mechanics":[7],"by":[8,46],"making":[9],"explicit":[10],"what":[11],"are":[12,32],"\\emph{operational}":[14],"objects":[15],"subject":[16,51],"to":[17,76,115],"relaxation:":[18],"local":[20,29],"time":[21,30],"statistics":[22,31],"of":[23,37,52,63,83,87,92,103,136],"recorded":[25],"signal":[26],"$Z(t)$.":[27],"These":[28],"simply":[33],"estimated":[35],"histograms":[36],"observations":[38],"$\\{Z(t_i)\\}_{i=1}^M$":[39],"performed":[40],"at":[41],"uniformly":[42],"random":[43],"times":[44],"$\\{t_i\\}_{i=1}^M$":[45],"a":[47,55,58,64,123],"clockless":[48],"observer.":[49,118],"The":[50,101],"prediction":[53],"is":[54,69,113,121],"belief":[56],"about":[57],"future":[59],"fresh":[60],"out-of-sample":[61],"reading":[62],"measurement":[65],"outcome":[66],"whose":[67,111],"distribution":[68],"inferred":[70],"from":[71],"mathematical":[73],"model":[74],"believed":[75],"be":[77],"true.":[78],"For":[79],"finite":[80],"bounded":[81],"systems":[82],"$N\\ge":[84],"1$":[85],"degrees":[86],"freedom":[88],"global":[89],"irreversible":[90],"predictions":[93,105],"can":[94],"occur":[95],"but":[96],"special":[97],"initial":[98],"conditions":[99],"exist.":[100],"form":[102],"depends":[106,148],"on":[107,149],"certain":[108],"loss":[109],"functions":[110],"choice":[112],"up":[114],"particular":[117],"Finally,":[119],"entropy":[120],"given":[122],"learning":[124],"interpretation":[125],"as":[126],"mutual":[127],"information":[128,151],"between":[129],"observer":[131],"and":[132],"unknown":[134],"past":[135],"system":[138],"under":[139],"consideration":[140],"and,":[141],"complete":[143],"generality,":[144],"its":[145],"stationary":[146],"value":[147],"available.":[152]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-02T00:00:00"}
