{"id":"https://openalex.org/W7203568372","doi":"https://doi.org/10.5281/zenodo.21935954","title":"Dynamical Black-Hole Entropy: One Ledger, Many Schedules","display_name":"Dynamical Black-Hole Entropy: One Ledger, Many Schedules","publication_year":2026,"publication_date":"2026-08-14","ids":{"openalex":"https://openalex.org/W7203568372","doi":"https://doi.org/10.5281/zenodo.21935954"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.21935954","doi":"https://doi.org/10.5281/zenodo.21935954","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.21935954","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.21935954","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058230647","display_name":"Fabio Zander","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zander, Fabio","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0000-0625-6021","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5058230647"],"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/T10025","display_name":"Black Holes and Theoretical Physics","score":0.9804999828338623,"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/T10025","display_name":"Black Holes and Theoretical Physics","score":0.9804999828338623,"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/T10095","display_name":"Cosmology and Gravitation Theories","score":0.0024999999441206455,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"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/T10744","display_name":"Astrophysical Phenomena and Observations","score":0.0020000000949949026,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"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/higher-derivative-gravity","display_name":"higher-derivative gravity","score":0.7760000228881836},{"id":"https://openalex.org/keywords/page-time","display_name":"Page time","score":0.8569999933242798}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7275999784469604},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5976999998092651},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5547999739646912},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.4404999911785126},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.3776000142097473},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3734000027179718},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.3443000018596649},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.31949999928474426},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.31709998846054077},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3163999915122986},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.31439998745918274},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3138999938964844},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.29809999465942383},{"id":"https://openalex.org/C146846114","wikidata":"https://www.wikidata.org/wiki/Q901448","display_name":"Einstein","level":2,"score":0.28679999709129333},{"id":"https://openalex.org/C166437778","wikidata":"https://www.wikidata.org/wiki/Q50695","display_name":"Quadratic function","level":3,"score":0.2761000096797943},{"id":"https://openalex.org/C207221997","wikidata":"https://www.wikidata.org/wiki/Q938614","display_name":"Affine combination","level":3,"score":0.27320000529289246},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.27219998836517334},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.27079999446868896},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2700999975204468},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.2517000138759613},{"id":"https://openalex.org/C204707403","wikidata":"https://www.wikidata.org/wiki/Q1152398","display_name":"Canonical form","level":2,"score":0.25}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.21935954","doi":"https://doi.org/10.5281/zenodo.21935954","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.21935954","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.21935955","doi":"https://doi.org/10.5281/zenodo.21935955","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.21935955","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.21935954","doi":"https://doi.org/10.5281/zenodo.21935954","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.21935954","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4403064898","https://openalex.org/W4409126439","https://openalex.org/W3121353773","https://openalex.org/W4400975983","https://openalex.org/W7106506862","https://openalex.org/W4415059650","https://openalex.org/W7160441405","https://openalex.org/W7169515504","https://openalex.org/W4395029472","https://openalex.org/W4389821577"],"abstract_inverted_index":{"Abstract:":[0],"All":[1],"admissible":[2],"dynamical":[3],"black-hole":[4],"entropy":[5],"prescriptions":[6],"at":[7,144],"four":[8],"derivatives":[9],"share":[10],"a":[11,82,96,110,127,150,158,163],"single":[12,83],"normalized":[13],"retardation":[14],"kernel,":[15],"K(s)=\u03bae\u2212\u03basK(s)=\\kappa":[16],"e^{-\\kappa":[17],"s}":[18],"K(s)=\u03bae\u2212\u03bas.":[19],"Its":[20],"zeroth":[21],"moment":[22,64],"-":[23,24,38,90,91,101,102],"equal":[25],"to":[26,78],"unity,":[27],"and":[28,73,95,103,147,162],"forced":[29],"by":[30],"the":[31,34,40,56,67,71,105,118,122,132,154,167,171],"identity":[32,69],"of":[33,70,131,166],"underlying":[35,170],"booking":[36,57],"operators":[37],"carries":[39,54],"invariant":[41],"total":[42],"(one":[43],"ledger);":[44],"its":[45],"first":[46],"moment,":[47],"1/\u03ba1/\\kappa":[48],"1/\u03ba":[49],"plus":[50],"prescription-specific":[51],"clock":[52,120],"shifts,":[53],"only":[55],"time":[58,156],"(many":[59],"schedules).":[60],"We":[61],"derive":[62],"this":[63],"structure":[65],"from":[66],"affine":[68,135],"Hollands-Wald-Zhang":[72],"Bonetto-Pound-Sam":[74],"operators,":[75],"extend":[76],"it":[77],"second":[79,145],"order,":[80],"where":[81],"quadratic":[84],"kernel":[85],"family":[86],"on":[87,109],"rates":[88],"emerges":[89],"an":[92],"instantaneous":[93],"dent":[94],"retarded":[97],"diagonal":[98],"\u03b8(2)=\u03ba\u22121(K\u2217\u03c32)\\theta^{(2)}=\\kappa^{-1}(K*\\sigma^2)":[99],"\u03b8(2)=\u03ba\u22121(K\u2217\u03c32)":[100],"compute":[104],"complete":[106],"Riemann-squared-sector":[107],"ledger":[108],"tidally":[111],"deformed":[112],"Schwarzschild":[113],"horizon:":[114],"S\u03bb3(v)=4\u03c0\u03bb3/G\u2212(\u03bb3/GM)A\u02d9(v)S_{\\lambda_3}(v)=4\\pi\\lambda_3/G-(\\lambda_3/GM)\\dot{A}(v)":[115],"S\u03bb3(v)=4\u03c0\u03bb3/G\u2212(\u03bb3/GM)A\u02d9(v),":[116],"so":[117],"higher-derivative":[119],"reads":[121],"Einstein":[123],"heating":[124],"rate.":[125],"As":[126],"closed":[128],"advanced-time":[129],"specialization":[130],"known":[133],"first-order":[134],"relation":[136],"(Hollands-Wald-Zhang;":[137],"Visser-Yan),":[138],"we":[139],"obtain":[140],"AAH(v)=AEH(v)\u2212\u03ba\u22121A\u02d9EH(v)A_{AH}(v)=A_{EH}(v)-\\kappa^{-1}\\dot{A}_{EH}(v)":[141],"AAH(v)=AEH(v)\u2212\u03ba\u22121A\u02d9EH(v),":[142],"exact":[143],"order":[146],"multipole-blind.":[148],"Applications:":[149],"prescription-robustness":[151],"statement":[152],"for":[153],"Page":[155],"with":[157],"sharp":[159],"eight-derivative":[160],"boundary,":[161],"classical-geometric":[164],"test":[165],"interior-independence":[168],"assumption":[169],"firewall":[172],"argument.":[173]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-08-17T00:00:00"}