{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,13]],"date-time":"2025-09-13T16:44:37Z","timestamp":1757781877480,"version":"3.37.3"},"reference-count":47,"publisher":"IOP Publishing","issue":"23","license":[{"start":{"date-parts":[[2024,11,1]],"date-time":"2024-11-01T00:00:00Z","timestamp":1730419200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2024,11,1]],"date-time":"2024-11-01T00:00:00Z","timestamp":1730419200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100013168","name":"Istituto Nazionale di Fisica Nucleare","doi-asserted-by":"crossref","award":["GAST"],"award-info":[{"award-number":["GAST"]}],"id":[{"id":"10.13039\/501100013168","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Class. Quantum Grav."],"published-print":{"date-parts":[[2024,12,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We explore nonequilibrium features of certain operator algebras which appear in quantum gravity. The algebra of observables in a black hole background is a Type<jats:inline-formula><jats:tex-math\/><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\"><mml:mrow><mml:msub><mml:mrow><mml:mi>II<\/mml:mi><\/mml:mrow><mml:mi mathvariant=\"normal\">\u221e<\/mml:mi><\/mml:msub><\/mml:mrow><\/mml:math><\/jats:inline-formula>von Neumann algebra. We discuss how this algebra can be coupled to the algebra of observable of an infinite reservoir within the canonical ensemble, aiming to induce nonequilibrium dynamics. The resulting dynamics can lead the system towards a nonequilibrium steady state which can be characterized through modular theory. Within this framework we address the definition of entropy production and its relationship to relative entropy, alongside exploring other applications.<\/jats:p>","DOI":"10.1088\/1361-6382\/ad85bf","type":"journal-article","created":{"date-parts":[[2024,10,10]],"date-time":"2024-10-10T22:57:41Z","timestamp":1728601061000},"page":"235006","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["On the nonequilibrium dynamics of gravitational algebras"],"prefix":"10.1088","volume":"41","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9940-3250","authenticated-orcid":true,"given":"Michele","family":"Cirafici","sequence":"first","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2024,11,1]]},"reference":[{"article-title":"The centaur-algebra of observables","year":"2023","author":"Aguilar-Gutierrez","key":"cqgad85bfbib1"},{"article-title":"Crossed product algebras and generalized entropy for subregions","year":"2023","author":"Ali Ahmad","key":"cqgad85bfbib2"},{"article-title":"Semifinite von Neumann algebras in gauge theory and gravity","year":"2024","author":"Ali Ahmad","key":"cqgad85bfbib3"},{"key":"cqgad85bfbib4","doi-asserted-by":"publisher","first-page":"JHEP12(2019)063","DOI":"10.1007\/JHEP12(2019)063","article-title":"The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole","author":"Almheiri","year":"2019","journal-title":"J. High Energy Phys."},{"key":"cqgad85bfbib5","doi-asserted-by":"publisher","first-page":"JHEP05(2020)013","DOI":"10.1007\/JHEP05(2020)013","article-title":"Replica Wormholes and the Entropy of Hawking Radiation","author":"Almheiri","year":"2020","journal-title":"J. High Energy Phys."},{"key":"cqgad85bfbib6","first-page":"pp 1","article-title":"Topics in nonequilibrium quantum statistical mechanics","author":"Aschbacher","year":"2006"},{"key":"cqgad85bfbib7","doi-asserted-by":"publisher","first-page":"JHEP06(2023)197","DOI":"10.1007\/JHEP06(2023)197","article-title":"Algebra of operators in an AdS-Rindler wedge","author":"Bahiru","year":"2023","journal-title":"J. High Energy Phys."},{"article-title":"Algebras and their Covariant representations in quantum gravity","year":"2023","author":"Bahiru","key":"cqgad85bfbib8"},{"year":"1996","author":"Bratteli","key":"cqgad85bfbib9"},{"article-title":"Large N algebras and generalized entropy","year":"2022","author":"Chandrasekaran","key":"cqgad85bfbib10"},{"key":"cqgad85bfbib11","doi-asserted-by":"publisher","first-page":"JHEP02(2023)082","DOI":"10.1007\/JHEP02(2023)082","article-title":"An algebra of observables for de Sitter space","author":"Chandrasekaran","year":"2023","journal-title":"J. High Energy Phys."},{"key":"cqgad85bfbib12","doi-asserted-by":"crossref","DOI":"10.1007\/JHEP11(2024)089","article-title":"Fluctuation theorems, quantum channels and gravitational algebras","author":"Cirafici","year":"2024"},{"key":"cqgad85bfbib13","doi-asserted-by":"publisher","first-page":"JHEP01(2015)073","DOI":"10.1007\/JHEP01(2015)073","article-title":"Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime","author":"Engelhardt","year":"2015","journal-title":"J. High Energy Phys."},{"article-title":"Algebraic ER = EPR and complexity transfer","year":"2023","author":"Engelhardt","key":"cqgad85bfbib14"},{"author":"Fewster","key":"cqgad85bfbib15","article-title":"Quantum reference frames, measurement schemes and the type of local algebras in quantum field theory"},{"key":"cqgad85bfbib16","doi-asserted-by":"publisher","first-page":"JHEP08(2023)111","DOI":"10.1007\/JHEP08(2023)111","article-title":"Information loss, mixing and emergent Type III1 factors","author":"Furuya","year":"2023","journal-title":"J. High Energy Phys."},{"article-title":"Large N von Neumann algebras and the renormalization of Newton\u2019s constant","year":"2023","author":"Gesteau","key":"cqgad85bfbib17"},{"article-title":"Emergent spacetime and the ergodic hierarchy","year":"2023","author":"Gesteau","key":"cqgad85bfbib18"},{"article-title":"Entanglement, observers and cosmology: a view from von Neumann U","year":"2023","author":"Gomez","key":"cqgad85bfbib19"},{"key":"cqgad85bfbib20","doi-asserted-by":"publisher","first-page":"829","DOI":"10.1023\/A:1019818909696","article-title":"Mathematical theory of non-equilibrium quantum statistical Mechanics","volume":"108","author":"Jak\u0161ic\u012c","year":"2002","journal-title":"J. Stat. Phys."},{"key":"cqgad85bfbib21","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1090\/conm\/327\/05813","article-title":"A note on the entropy production formula","volume":"327","author":"Jak\u0161ic\u012c","year":"2003","journal-title":"Contemp. Math."},{"key":"cqgad85bfbib22","doi-asserted-by":"publisher","first-page":"JHEP12(2023)020","DOI":"10.1007\/JHEP12(2023)020","article-title":"Generalized entropy for general subregions in quantum gravity","author":"Jensen","year":"2023","journal-title":"J. High Energy Phys."},{"key":"cqgad85bfbib23","doi-asserted-by":"publisher","DOI":"10.1016\/j.nuclphysb.2024.116453","article-title":"Crossed products, extended phase spaces and the resolution of entanglement singularities","volume":"999","author":"Klinger","year":"2024","journal-title":"Nucl. Phys. B"},{"key":"cqgad85bfbib24","doi-asserted-by":"publisher","first-page":"JHEP06(2023)067","DOI":"10.1007\/JHEP06(2023)067","article-title":"von Neumann algebras in JT gravity","author":"Kolchmeyer","year":"2023","journal-title":"J. High Energy Phys."},{"article-title":"State-independent black hole interiors from the crossed product","year":"2023","author":"Krishnan","key":"cqgad85bfbib25"},{"article-title":"Generalized black hole entropy is von Neumann entropy","year":"2023","author":"Kudler-Flam","key":"cqgad85bfbib26"},{"article-title":"A covariant regulator for entanglement entropy: proofs of the Bekenstein bound and QNEC","year":"2023","author":"Kudler-Flam","key":"cqgad85bfbib27"},{"key":"cqgad85bfbib28","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.108.086019","article-title":"Causal connectability between quantum systems and the black hole interior in holographic duality","volume":"108","author":"Leutheusser","year":"2023","journal-title":"Phys. Rev. D"},{"key":"cqgad85bfbib29","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.108.086020","article-title":"Emergent times in holographic duality","volume":"108","author":"Leutheusser","year":"2023","journal-title":"Phys. Rev. D"},{"article-title":"Subalgebra-subregion duality: emergence of space and time in holography","year":"2022","author":"Leutheusser","key":"cqgad85bfbib30"},{"key":"cqgad85bfbib31","doi-asserted-by":"publisher","first-page":"JHEP04(2003)021","DOI":"10.1088\/1126-6708\/2003\/04\/021","article-title":"Eternal black holes in anti-de Sitter","author":"Maldacena","year":"2003","journal-title":"J. High Energy Phys."},{"key":"cqgad85bfbib32","doi-asserted-by":"publisher","first-page":"JHEP08(2016)106","DOI":"10.1007\/JHEP08(2016)106","article-title":"A bound on chaos","author":"Maldacena","year":"2016","journal-title":"J. High Energy Phys."},{"key":"cqgad85bfbib33","doi-asserted-by":"publisher","first-page":"JHEP01(2024)112","DOI":"10.1007\/JHEP01(2024)112","article-title":"Local Poincar\u00e9 algebra from quantum chaos","author":"Ouseph","year":"2024","journal-title":"J. High Energy Phys."},{"key":"cqgad85bfbib34","doi-asserted-by":"publisher","first-page":"JHEP10(2013)212","DOI":"10.1007\/JHEP10(2013)212","article-title":"An infalling observer in AdS\/CFT","author":"Papadodimas","year":"2013","journal-title":"J. High Energy Phys."},{"key":"cqgad85bfbib35","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.89.086010","article-title":"State-dependent bulk-boundary maps and black hole complementarity","volume":"89","author":"Papadodimas","year":"2014","journal-title":"Phys. Rev. D"},{"key":"cqgad85bfbib36","doi-asserted-by":"publisher","first-page":"JHEP09(2020)002","DOI":"10.1007\/JHEP09(2020)002","article-title":"Entanglement wedge reconstruction and the information paradox","author":"Penington","year":"2020","journal-title":"J. High Energy Phys."},{"key":"cqgad85bfbib37","doi-asserted-by":"publisher","first-page":"JHEP03(2022)205","DOI":"10.1007\/JHEP03(2022)205","article-title":"Replica wormholes and the black hole interior","author":"Penington","year":"2022","journal-title":"J. High Energy Phys."},{"article-title":"Algebras and states in JT gravity","year":"2023","author":"Penington","key":"cqgad85bfbib38"},{"author":"Ruelle","key":"cqgad85bfbib39","article-title":"Topics in quantum statistical mechanics and operator algebras"},{"key":"cqgad85bfbib40","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1023\/A:1018618704438","article-title":"Natural nonequilibrium states in quantum statistical mechanics","volume":"98","author":"Ruelle","year":"2000","journal-title":"J. Stat. Phys."},{"key":"cqgad85bfbib41","doi-asserted-by":"publisher","first-page":"701","DOI":"10.1142\/S0129055X02001296","article-title":"How should one define entropy production for nonequilibrium quantum spin systems?","volume":"14","author":"Ruelle","year":"2002","journal-title":"Rev. Math. Phys."},{"article-title":"Notes on the Type classification of von Neumann algebras","year":"2023","author":"Sorce","key":"cqgad85bfbib42"},{"key":"cqgad85bfbib43","doi-asserted-by":"publisher","first-page":"JHEP12(2023)079","DOI":"10.1007\/JHEP12(2023)079","article-title":"An intuitive construction of modular flow","author":"Sorce","year":"2023","journal-title":"J. High Energy Phys."},{"key":"cqgad85bfbib44","doi-asserted-by":"publisher","first-page":"JHEP03(2014)067","DOI":"10.1007\/JHEP03(2014)067","article-title":"Black holes and the butterfly effect","author":"Shenker","year":"2014","journal-title":"J. High Energy Phys."},{"key":"cqgad85bfbib45","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.90.045003","article-title":"APS medal for exceptional achievement in research: invited article on entanglement properties of quantum field theory","volume":"90","author":"Witten","year":"2018","journal-title":"Rev. Mod. Phys."},{"article-title":"Why does quantum field theory in curved spacetime make sense? And what happens to the algebra of observables in the thermodynamic limit?","year":"2021","author":"Witten","key":"cqgad85bfbib46"},{"key":"cqgad85bfbib47","doi-asserted-by":"publisher","first-page":"JHEP10(2022)008","DOI":"10.1007\/JHEP10(2022)008","article-title":"Gravity and the crossed product","author":"Witten","year":"2022","journal-title":"J. High Energy Phys."}],"container-title":["Classical and Quantum Gravity"],"original-title":[],"link":[{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/ad85bf","content-type":"text\/html","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/ad85bf\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/ad85bf","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/ad85bf\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/ad85bf\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/ad85bf\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/ad85bf\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"similarity-checking"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/ad85bf\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,29]],"date-time":"2024-11-29T12:53:31Z","timestamp":1732884811000},"score":1,"resource":{"primary":{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/ad85bf"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,1]]},"references-count":47,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2024,11,1]]},"published-print":{"date-parts":[[2024,12,5]]}},"URL":"https:\/\/doi.org\/10.1088\/1361-6382\/ad85bf","relation":{},"ISSN":["0264-9381","1361-6382"],"issn-type":[{"type":"print","value":"0264-9381"},{"type":"electronic","value":"1361-6382"}],"subject":[],"published":{"date-parts":[[2024,11,1]]},"assertion":[{"value":"On the nonequilibrium dynamics of gravitational algebras","name":"article_title","label":"Article Title"},{"value":"Classical and Quantum Gravity","name":"journal_title","label":"Journal Title"},{"value":"paper","name":"article_type","label":"Article Type"},{"value":"\u00a9 2024 The Author(s). Published by IOP Publishing Ltd","name":"copyright_information","label":"Copyright Information"},{"value":"2024-07-18","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2024-10-10","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2024-11-01","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}