{"id":"https://openalex.org/W7225754616","doi":"https://doi.org/10.5281/zenodo.24113704","title":"Broken Time Reversal Invariance in the Tsallis, Kaniadakis Cases and Correlations","display_name":"Broken Time Reversal Invariance in the Tsallis, Kaniadakis Cases and Correlations","publication_year":2026,"publication_date":"2026-11-10","ids":{"openalex":"https://openalex.org/W7225754616","doi":"https://doi.org/10.5281/zenodo.24113704"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24113704","doi":"https://doi.org/10.5281/zenodo.24113704","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24113704","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24113704","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5152653323","display_name":"Francesco Rocco Ruggeri","orcid":"https://orcid.org/0000-0002-4049-8857","observed_orcids":["https://orcid.org/0000-0002-4049-8857"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ruggeri, Francesco R.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5152653323"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9990000128746033,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9990000128746033,"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.0005000000237487257,"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/T11270","display_name":"Complex Systems and Time Series Analysis","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[],"concepts":[{"id":"https://openalex.org/C152754458","wikidata":"https://www.wikidata.org/wiki/Q142270","display_name":"T-symmetry","level":3,"score":0.682200014591217},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6177999973297119},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.609499990940094},{"id":"https://openalex.org/C204795200","wikidata":"https://www.wikidata.org/wiki/Q903282","display_name":"Symmetry breaking","level":2,"score":0.5694000124931335},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.42399999499320984},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.40790000557899475},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.4059999883174896},{"id":"https://openalex.org/C2778348673","wikidata":"https://www.wikidata.org/wiki/Q739302","display_name":"Production (economics)","level":2,"score":0.37529999017715454},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.34860000014305115},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3449999988079071},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.3352999985218048},{"id":"https://openalex.org/C1924353","wikidata":"https://www.wikidata.org/wiki/Q1042929","display_name":"Elastic scattering","level":3,"score":0.33410000801086426},{"id":"https://openalex.org/C58721731","wikidata":"https://www.wikidata.org/wiki/Q1105337","display_name":"Explicit symmetry breaking","level":4,"score":0.3287999927997589},{"id":"https://openalex.org/C121704057","wikidata":"https://www.wikidata.org/wiki/Q352070","display_name":"Collision","level":2,"score":0.3280999958515167},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.2992999851703644},{"id":"https://openalex.org/C117220453","wikidata":"https://www.wikidata.org/wiki/Q5172842","display_name":"Correlation","level":2,"score":0.2955999970436096},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2922999858856201}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24113704","doi":"https://doi.org/10.5281/zenodo.24113704","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24113704","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},{"id":"doi:10.5281/zenodo.24113705","doi":"https://doi.org/10.5281/zenodo.24113705","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24113705","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"doi:10.5281/zenodo.24113704","doi":"https://doi.org/10.5281/zenodo.24113704","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24113704","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Newton\u2019s":[0],"second":[1],"law":[2],"is":[3,9,47,71,112,147,216],"time":[4,19,101,169],"reversal":[5,20,102,170],"invariant,":[6],"but":[7],"it":[8,125,178,202],"well-known":[10],"that":[11,15,59,120,144,156,219,255,286,293],"in":[12,39,90,119,161,231,280],"Newtonian":[13],"mechanics":[14],"one":[16,97],"may":[17,250,296],"have":[18,100,270],"breaking":[21,35],"processes":[22],"such":[23,197],"as":[24,261],"heat":[25,191],"production":[26],"due":[27,193,302],"to":[28,32,142,149,194,208,217,225,253,269,303,310],"friction.":[29],"These":[30],"seem":[31],"involve":[33],"symmetry":[34,49,111,171],"processes.":[36],"For":[37],"example,":[38],"the":[40,55,67,91,110,220,228,232,236,275,281,287,294],"Maxwell-Boltzmann":[41,282],"two":[42,63],"body":[43,64],"scattering":[44,53],"scenario,":[45],"there":[46],"a":[48,117,135,164,188,247,299],"involved":[50],"with":[51],"elastic":[52,105,174,276],"and":[54,93,131,289],"uniform":[56],"distribution":[57],"indicates":[58],"any":[60],"energy":[61,233],"conserving":[62],"collision":[65,277],"has":[66],"same":[68],"probability.":[69],"This":[70],"quantitatively":[72,305],"expressed":[73],"through":[74],"p(ei)p(ej)":[75],"=":[76],"p(ek)p(el)":[77],"if":[78],"ei+ej=ek+el.":[79],"If":[80],"p(ei)p(ej)=p(ek)p(el)":[81],"for":[82,86,104,129,172,179,205],"ei*ej":[83,166],"=ek*el":[84],"((1))":[85,121,185],"e/T>>1,":[87],"(which":[88,257],"holds":[89],"Tsallis":[92,288],"Kaniadakis":[94,290],"cases),":[95],"then":[96],"does":[98,126,158,266],"not":[99,127,159,267],"invariance":[103],"scattering.":[106],"In":[107,138,187],"other":[108],"words,":[109],"gone.":[113],"There":[114],"is,":[115],"however,":[116],"correlation":[118,146,198,248],"exists,":[122],"even":[123],"though":[124],"hold":[128],"before":[130],"after":[132],"situations":[133],"of":[134,213,222,235,263],"2-body":[136],"collision.":[137],"(1),":[139],"we":[140,258],"tried":[141],"show":[143,292],"this":[145,214],"enough":[148,252],"ensure":[150,254],"an":[151,173,180,206],"equilibrium":[152,207],"scenario":[153,189],"which":[154,167,249],"means":[155],"p(ei)":[157],"change":[160],"time.":[162],"As":[163],"result,":[165],"breaks":[168],"collision,":[175],"can":[176],"restore":[177],"entire":[181],"system":[182],"because":[183],"correlations":[184,304],"exist.":[186],"like":[190],"loss":[192],"friction,":[195],"no":[196],"exists":[199],"anywhere":[200],"making":[201],"seemingly":[203],"impossible":[204],"result.":[209],"The":[210],"basic":[211],"purpose":[212],"note":[215],"suggest":[218],"approach":[221],"finding":[223],"solutions":[224,309],"p(ei)p(ej)=p(ek)p(el),":[226],"using":[227],"simplest":[229],"functions":[230],"variable":[234],"constraint,":[237],"i.e.":[238],"ei":[239,244,308],"from":[240],"Sum":[241],"over":[242],"i":[243],"p(ei)=Eave,":[245],"introduces":[246],"be":[251,297],"p(ei,t)=p(ei)":[256],"loosely":[259],"take":[260],"definition":[262],"equilibrium).":[264],"One":[265],"need":[268],"product":[271],"probabilities":[272],"conserved":[273],"at":[274,298],"level":[278],"(as":[279],"case).":[283],"It":[284],"seems":[285],"cases":[291],"balance":[295],"larger":[300],"scale":[301],"described":[306],"by":[307],"p(ei)p(ej)=p(ek)p(el).":[311]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-11T00:00:00"}