{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,29]],"date-time":"2026-06-29T19:14:42Z","timestamp":1782760482832,"version":"3.54.5"},"reference-count":77,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,5]],"date-time":"2025-02-05T00:00:00Z","timestamp":1738713600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China (NSFC)","award":["12375057"],"award-info":[{"award-number":["12375057"]}]},{"name":"National Natural Science Foundation of China (NSFC)","award":["11947301"],"award-info":[{"award-number":["11947301"]}]},{"name":"National Natural Science Foundation of China (NSFC)","award":["12047502"],"award-info":[{"award-number":["12047502"]}]},{"name":"Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan)","award":["12375057"],"award-info":[{"award-number":["12375057"]}]},{"name":"Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan)","award":["11947301"],"award-info":[{"award-number":["11947301"]}]},{"name":"Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan)","award":["12047502"],"award-info":[{"award-number":["12047502"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, we review some methods that have tried to solve the information loss problem. In particular, we revisit the solution based on Hawking radiation as tunneling and provide a detailed statistical interpretation of the black hole entropy in terms of the quantum tunneling probability of Hawking radiation from the black hole. In addition, we show that black hole evaporation is governed by a time-dependent Schr\u00f6dinger equation that sends pure states into pure states rather than into mixed states (Hawking had originally established that the final result would be mixed states). This is further confirmation of the fact that black hole evaporation is unitary.<\/jats:p>","DOI":"10.3390\/e27020167","type":"journal-article","created":{"date-parts":[[2025,2,5]],"date-time":"2025-02-05T07:44:59Z","timestamp":1738741499000},"page":"167","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["The Information Loss Problem and Hawking Radiation as Tunneling"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9128-1458","authenticated-orcid":false,"given":"Baocheng","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1999-4503","authenticated-orcid":false,"given":"Christian","family":"Corda","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Physics, SUNY Polytechnic Institute, Utica, NY 13502, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qingyu","family":"Cai","sequence":"additional","affiliation":[{"name":"Center for Theoretical Physics, Hainan University, Haikou 570228, China"},{"name":"School of Information and Communication Engineering, Hainan University, Haikou 570228, China"},{"name":"Peng Huanwu Center for Fundamental Theory, Hefei 230026, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1038\/248030a0","article-title":"Black hole explosions?","volume":"248","author":"Hawking","year":"1974","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/BF02345020","article-title":"Particle creation by black holes","volume":"43","author":"Hawking","year":"1975","journal-title":"Comm. Math. Phys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2460","DOI":"10.1103\/PhysRevD.14.2460","article-title":"Breakdown of predictability in gravitational collapse","volume":"14","author":"Hawking","year":"1976","journal-title":"Phys. Rev. D"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"084013","DOI":"10.1103\/PhysRevD.72.084013","article-title":"Information loss in black holes","volume":"72","author":"Hawking","year":"2005","journal-title":"Phys. Rev. D"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"092002","DOI":"10.1088\/1361-6633\/aa778e","article-title":"Information loss in black hole","volume":"80","author":"Unruh","year":"2017","journal-title":"Rep. Prog. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1103\/RevModPhys.76.93","article-title":"Information loss","volume":"76","author":"Peres","year":"2004","journal-title":"Rev. Mod. Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"063","DOI":"10.1007\/JHEP12(2019)063","article-title":"The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole","volume":"12","author":"Almheiri","year":"2019","journal-title":"JHEP"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"002","DOI":"10.1007\/JHEP09(2020)002","article-title":"Entanglement wedge reconstruction and the information paradox","volume":"9","author":"Penington","year":"2020","journal-title":"JHEP"},{"key":"ref_9","first-page":"123","article-title":"Black holes and quantum information","volume":"2","author":"Maldacena","year":"2020","journal-title":"Nat. Rev."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"035002","DOI":"10.1103\/RevModPhys.93.035002","article-title":"The entropy of Hawking radiation","volume":"93","author":"Almheiri","year":"2021","journal-title":"Rev. Mod. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/0370-2693(87)91320-7","article-title":"The unitarity puzzle and Planck mass stable particles","volume":"191","author":"Aharonov","year":"1987","journal-title":"Phys. Lett. B"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2015.10.007","article-title":"Black hole remnants and the information loss paradox","volume":"603","author":"Chen","year":"2015","journal-title":"Phys. Rep."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1221","DOI":"10.1103\/PhysRevLett.62.1221","article-title":"Discrete gauge symmetry in continuum theories","volume":"62","author":"Krauss","year":"1989","journal-title":"Phys. Rev. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"231301","DOI":"10.1103\/PhysRevLett.116.231301","article-title":"Soft Hair on Black Holes","volume":"116","author":"Hawking","year":"2016","journal-title":"Phys. Rev. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"008","DOI":"10.1088\/1126-6708\/2004\/02\/008","article-title":"Unitarity of black hole evaporation in final-state projection models","volume":"0402","author":"Horowitz","year":"2004","journal-title":"JHEP"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"062","DOI":"10.1007\/JHEP02(2013)062","article-title":"Black Holes: Complementarity or Firewalls?","volume":"02","author":"Almheiri","year":"2013","journal-title":"JHEP"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"781","DOI":"10.1002\/prop.201300020","article-title":"Cool horizons for entangled black holes","volume":"61","author":"Maldacena","year":"2013","journal-title":"Fortsch. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Polchinski, J. (2017). The Black Hole Information Problem. arXiv.","DOI":"10.1142\/9789813149441_0006"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"015002","DOI":"10.1103\/RevModPhys.88.015002","article-title":"Jerusalem lectures on black holes and quantum information","volume":"88","author":"Harlow","year":"2016","journal-title":"Rev. Mod. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"092001","DOI":"10.1088\/1361-6633\/aa77cc","article-title":"The black hole information problem: Past, present, and future","volume":"80","author":"Marolf","year":"2017","journal-title":"Rep. Prog. Phys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"5042","DOI":"10.1103\/PhysRevLett.85.5042","article-title":"Hawking radiation as tunneling","volume":"85","author":"Parikh","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1016\/j.physletb.2009.03.082","article-title":"Hidden messenger revealed in Hawking radiation: A resolution to the paradox of black hole information loss","volume":"675","author":"Zhang","year":"2009","journal-title":"Phys. Lett. B"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1341014","DOI":"10.1142\/S0218271813410149","article-title":"Information conservation is fundamental: Recovering the lost information in Harking radiation","volume":"22","author":"Zhang","year":"2013","journal-title":"Int. J. Mod. Phys."},{"key":"ref_24","first-page":"037","article-title":"Hawking radiation as tunneling through the quantum horizon","volume":"0509","author":"Arzano","year":"2015","journal-title":"JHEP"},{"key":"ref_25","unstructured":"Nielsen, M.A., and Chuang, I.L. (2000). Quantum Computation and Quantum Information, Cambridge University Press."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1103\/PhysRevD.13.191","article-title":"Black holes and thermodynamics","volume":"13","author":"Hawking","year":"1976","journal-title":"Phys. Rev. D"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"124036","DOI":"10.1103\/PhysRevD.82.124036","article-title":"Band-aid for information loss from black holes","volume":"82","author":"Israel","year":"2010","journal-title":"Phys. Rev. D"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/j.nuclphysb.2016.02.030","article-title":"Information-carrying Hawking radiation and the number of microstate for a black hole","volume":"905","author":"Cai","year":"2016","journal-title":"Nucl. Phys. B"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1007\/BF02762768","article-title":"The quantum mass spectrum of the Kerr black hole","volume":"11","author":"Bekenstein","year":"1974","journal-title":"Lett. Nuovo C."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1632","DOI":"10.1134\/S0040577922110083","article-title":"Quantum oscillations in the black hole horizon","volume":"213","author":"Corda","year":"2022","journal-title":"Theor. Math. Phys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1007\/JHEP08(2010)089","article-title":"Insights and possible resolution to the information loss paradox via the tunneling picture","volume":"2010","author":"Singleton","year":"2010","journal-title":"JHEP"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1016\/j.aop.2010.11.015","article-title":"Entropy is conserved in Hawking radiation as tunneling: A revisit of the black hole information loss paradox","volume":"326","author":"Zhang","year":"2011","journal-title":"Ann. Phys."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"20002","DOI":"10.1209\/0295-5075\/94\/20002","article-title":"Noncommutative information is revealed from Hawking radiation as tunneling","volume":"94","author":"Zhang","year":"2011","journal-title":"EPL"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"020401","DOI":"10.1088\/0256-307X\/29\/2\/020401","article-title":"Entropy Conservation in the Transition of Schwarzschild-de Sitter Space to de Sitter Space through Tunneling","volume":"29","author":"Zhang","year":"2012","journal-title":"Chin. Phys. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/s10509-012-1028-3","article-title":"Fading Hawking Radiation","volume":"340","author":"Sakalli","year":"2012","journal-title":"Astrophys. Space Sci."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1139\/p2012-035","article-title":"Planck-scale nonthermal correlations in a noncommutative geometry inspired Vaidya black hole","volume":"90","author":"Mehdipour","year":"2012","journal-title":"Can. J. Phys."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1057","DOI":"10.1007\/s11434-014-0187-8","article-title":"Correlation, entropy, and information transfer in black hole radiation","volume":"59","author":"Zhang","year":"2014","journal-title":"Chin. Sci. Bull."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1140\/epjc\/s10052-015-3272-5","article-title":"Recovering information of tunneling spectrum from Weakly Isolated Horizon","volume":"75","author":"Chen","year":"2015","journal-title":"Eur. Phys. J. C"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.physletb.2018.12.074","article-title":"Revisiting the tunneling of charged particles and information recovery from Kerr-Newman black holes","volume":"792","author":"Chen","year":"2019","journal-title":"Phys. Lett. B"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1140\/epjc\/s10052-019-7040-9","article-title":"Fermions and vector particles tunnelling from non-rotating weakly isolated horizons","volume":"79","author":"Chen","year":"2019","journal-title":"Eur. Phys. J. C"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.1088\/0253-6102\/71\/8\/1007","article-title":"Information Conservation in a Noncommutative Quantum Black Hole Based on Canonical Typicality","volume":"71","author":"He","year":"2019","journal-title":"Commun. Theor. Phys."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/j.cjph.2023.11.012","article-title":"Thermodynamics of a quantum corrected Reissner-Nordstr\u00f6m black hole","volume":"87","author":"Song","year":"2024","journal-title":"Chin. J. Phys."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.physletb.2009.06.004","article-title":"Information loss and entropy conservation in quantum corrected Hawking radiation","volume":"678","author":"Chen","year":"2009","journal-title":"Phys. Lett. B"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1140\/epjc\/s10052-010-1379-2","article-title":"Thermodynamics Inducing Massive Particles\u2019 Tunneling and Cosmic Censorship","volume":"68","author":"Zhang","year":"2010","journal-title":"Eur. Phys. J. C"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"071302","DOI":"10.1103\/PhysRevLett.107.071302","article-title":"Black hole evaporation rates without spacetime","volume":"107","author":"Braunstein","year":"2011","journal-title":"Phys. Rev. Lett."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1007\/s10714-010-1097-y","article-title":"An interpretation for the entropy of a black hole","volume":"43","author":"Zhang","year":"2011","journal-title":"Gen. Relativ. Gravit."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"2665","DOI":"10.1140\/epjc\/s10052-013-2665-6","article-title":"Black hole quantum spectrum","volume":"73","author":"Corda","year":"2013","journal-title":"Eur. Phys. J. C"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"165004","DOI":"10.1088\/0264-9381\/30\/16\/165004","article-title":"Dynamical evaporation of quantum horizons","volume":"30","author":"Pranzetti","year":"2013","journal-title":"Class. Quant. Grav."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"1450010","DOI":"10.1142\/S0219887814500108","article-title":"Absence of Black Holes Information Paradox in Group Field Cosmology","volume":"11","author":"Faizal","year":"2014","journal-title":"Int. J. Geom. Meth. Mod. Phys."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"008","DOI":"10.1007\/JHEP06(2013)008","article-title":"Effective state, Hawking radiation and quasi-normal modes for Kerr black holes","volume":"6","author":"Corda","year":"2013","journal-title":"JHEP"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"074","DOI":"10.1007\/JHEP05(2014)074","article-title":"Self-similarity, conservation of entropy\/bits and the black hole information puzzle","volume":"5","author":"Singleton","year":"2014","journal-title":"JHEP"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"527874","DOI":"10.1155\/2014\/527874","article-title":"Hawking radiation\u2014Quasi-normal modes correspondence and effective states for non-extremal Reissner-Nordstrom black holes","volume":"2014","author":"Corda","year":"2014","journal-title":"Adv. High Energy Phys."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1088\/0253-6102\/61\/3\/03","article-title":"One Hair Postulate for Hawking Radiation as Tunneling Process","volume":"61","author":"Dong","year":"2014","journal-title":"Commun. Theor. Phys."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.aop.2014.11.002","article-title":"Time dependent Schr\u00f6dinger equation for black hole evaporation: No information loss","volume":"353","author":"Corda","year":"2015","journal-title":"Ann. Phys."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"195007","DOI":"10.1088\/0264-9381\/32\/19\/195007","article-title":"Precise model of Hawking radiation from the tunnelling mechanism","volume":"32","author":"Corda","year":"2015","journal-title":"Class. Quant. Grav."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"867601","DOI":"10.1155\/2015\/867601","article-title":"Quasi-Normal Modes: The \u2018Electrons\u2019 of Black Holes as \u2018Gravitational Atoms\u2019? Implications for the Black Hole Information Puzzle","volume":"2015","author":"Corda","year":"2015","journal-title":"Adv. High Energy Phys."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/j.physletb.2016.05.079","article-title":"The third order correction on Hawking radiation and entropy conservation during black hole evaporation process","volume":"759","author":"Yan","year":"2016","journal-title":"Phys. Lett. B"},{"key":"ref_58","doi-asserted-by":"crossref","unstructured":"Silva, C.A.S., and Brito, F.A. (2017). Quantum Tunneling Radiation from Loop Quantum Black Holes and the Information Loss Paradox. Universe, 3.","DOI":"10.3390\/universe3020042"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"1850103","DOI":"10.1142\/S0217732318501031","article-title":"Hidden Messenger from Quantum Geometry: Towards Information Conservation in Quantum Gravity","volume":"33","author":"Guo","year":"2018","journal-title":"Mod. Phys. Lett. A"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"124016","DOI":"10.1103\/PhysRevD.105.124016","article-title":"Probability distribution for black hole evaporation","volume":"105","author":"Ghosal","year":"2022","journal-title":"Phys. Rev. D"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"138335","DOI":"10.1016\/j.physletb.2023.138335","article-title":"Quantum tunneling from Schwarzschild black hole in non-commutative gauge theory of gravity","volume":"848","author":"Touati","year":"2024","journal-title":"Phys. Lett. B"},{"key":"ref_62","doi-asserted-by":"crossref","unstructured":"Ming, X. (2024). Multipartite Correlations in Parikh\u2013Wilczek Non-Thermal Spectrum. Entropy, 26.","DOI":"10.3390\/e26080680"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"183001","DOI":"10.1088\/0264-9381\/28\/18\/183001","article-title":"Tunnelling Methods and Hawking\u2019s radiation: Achievements and prospects","volume":"28","author":"Vanzo","year":"2011","journal-title":"Class. Quant. Grav."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"064046","DOI":"10.1103\/PhysRevD.91.064046","article-title":"How big is a black hole?","volume":"91","author":"Christodoulou","year":"2015","journal-title":"Phys. Rev. D"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"081501","DOI":"10.1103\/PhysRevD.92.081501","article-title":"Entropy in the interior of a black hole and thermodynamics","volume":"91","author":"Zhang","year":"2015","journal-title":"Phys. Rev. D"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1016\/j.physletb.2017.09.035","article-title":"On the entropy associated with the interior of a black hole","volume":"773","author":"Zhang","year":"2017","journal-title":"Phys. Lett. B"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1016\/j.physletb.2016.12.027","article-title":"Infinite volume of noncommutative black hole wrapped by finite surface","volume":"765","author":"Zhang","year":"2017","journal-title":"Phys. Lett. B"},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"025401","DOI":"10.1088\/1572-9494\/ab6186","article-title":"A divergent volume for black holes calls for no \u2018firewall\u2019","volume":"72","author":"Zhang","year":"2020","journal-title":"Commun. Theor. Phys."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"1441002","DOI":"10.1142\/S0218271814410028","article-title":"Black holes as Gravitational Atoms","volume":"23","author":"Vaz","year":"2014","journal-title":"Int. J. Mod. Phys. D"},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"2300028","DOI":"10.1002\/prop.202300028","article-title":"Black hole spectra from Vaz\u2019s quantum gravitational collapse","volume":"2023","author":"Corda","year":"2023","journal-title":"Fortschr. Phys."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"095405","DOI":"10.1088\/1572-9494\/ace4b2","article-title":"Schr\u00f6dinger and Klein-Gordon theories of black holes from the quantization of the Oppenheimer and Snyder gravitational collapse","volume":"75","author":"Corda","year":"2023","journal-title":"Commun. Theor. Phys."},{"key":"ref_72","unstructured":"Hawking, S.W. (2014). Information Preservation and Weather Forecasting for Black Holes. arXiv."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"922","DOI":"10.2307\/1968902","article-title":"On a Stationary System With Spherical Symmetry Consisting of Many Gravitating Masses","volume":"40","author":"Einstein","year":"1939","journal-title":"Ann. Math. (Second Ser.)"},{"key":"ref_74","unstructured":"Mathur, S.D., and Mehta, M. (2024). The Fuzzball Paradigm. arXiv."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"3","DOI":"10.12942\/lrr-2011-3","article-title":"Analogue gravity","volume":"14","author":"Liberati","year":"2011","journal-title":"Living Rev. Relativ."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"688","DOI":"10.1038\/s41586-019-1241-0","article-title":"Observation of thermal Hawking radiation and its temperature in an analogue black hole","volume":"569","author":"Golubkov","year":"2019","journal-title":"Nature"},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"044006","DOI":"10.1103\/PhysRevD.87.044006","article-title":"Towards experimentally testing the paradox of black hole information loss","volume":"87","author":"Zhang","year":"2013","journal-title":"Phys. Rev. D"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/2\/167\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:27:18Z","timestamp":1760027238000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/2\/167"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,5]]},"references-count":77,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,2]]}},"alternative-id":["e27020167"],"URL":"https:\/\/doi.org\/10.3390\/e27020167","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,2,5]]}}}