The DOI matches its Crossref record; 13 of the 13 references it cites were found in a registry or an index.
Entropy Evaporated by a Black Hole
Abstract
It is shown that the entropy of the radiation evaporated by an uncharged, nonrotating black hole into vacuum in the course of its lifetime is approximately $\frac{4}{3}$ times the initial entropy of this black hole. Also considered is a thermodynamically reversible process in which an increase of black-hole entropy is equal to the decrease of the entropy of its surroundings. Implications of these results for the generalized second law of thermodynamics and for the interpretation of black-hole entropy are pointed out.
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In the citing paper
“For the evaporating black hole the Page time comes out to be 1/3 of the black hole lifetime. This fits with the following simple reasoning [33]. Radiating into a cold surrounding space is an irreversible process and the entropy of the radiation grows at twice the evaporation rate of the black hole.”
From Page curve for an evaporating black hole (2020) · cites this paper as [33]
In the citing paper
“From the above, one sees that the matter entropy rises twice as fast as the black hole entropy decreases, which is no coincidence (Zurek 1982; Fiola et al. 1994).”
From Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity (2023) · cites this paper as Zurek 1982
In the citing paper
“In fact, the numerical results indicate that S = κ 1 log( MR )+ κ 2 log( µR ) in one dimension; for the first time, we see a dependence on the infrared cutoff µ [6].”
From Entropy and area (1993) · cites this paper as [6]
Citations
Cites
Particle creation by black holes
Hawking, S. W. (1975) · Communications In Mathematical Physics · doi:10.1007/bf02345020 · Cited by 13,106
Bekenstein, J. D. (1973) · Physical Review D · doi:10.1103/physrevd.7.2333 · Cited by 7,555
HAWKING, S. W. (1974) · Nature · doi:10.1038/248030a0 · Cited by 5,669
Breakdown of predictability in gravitational collapse
Hawking, S. W. (1976) · Physical Review D · doi:10.1103/physrevd.14.2460 · Cited by 2,554
Black holes and thermodynamics
Hawking, S. W. (1976) · Physical Review D · doi:10.1103/physrevd.13.191 · Cited by 1,307
Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole
Page, D. N. (1976) · Physical Review D · doi:10.1103/physrevd.13.198 · Cited by 1,133
On particle creation by black holes
Wald, R. M. (1975) · Communications in Mathematical Physics · doi:10.1007/bf01609863 · Cited by 480
Black holes and thermal Green functions
Gibbons, G. W., & Perry, M. J. (1978) · Proceedings of the Royal Society of London A Mathematical and Physical Sciences · doi:10.1098/rspa.1978.0022 · Cited by 351
Acceleration radiation and the generalized second law of thermodynamics
Unruh, W. G., & Wald, R. M. (1982) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.25.942 · Cited by 347
Bekenstein, J. D. (1980) · Physics Today · doi:10.1063/1.2913906 · Cited by 209
Flagged first, then by citations
Research works printed but not linked: 3
- C. W. Misner, 1973, Graviation
- M. Planck, 1900, Verh. Dtsch. Phys. Ges., 2, 237
- R. Penrose, 1982, Quantum Gravity II
Cited by
Sorted by citations
Items 101–124 of 124
Globally hyperbolic evaporating black hole and the information loss issue
Pêgas, J. V. O., Landulfo, A. G. S., Matsas, G. E. A., & Vanzella, D. A. T. (2025) · Classical and Quantum Gravity · doi:10.1088/1361-6382/adb534 · Cited by 2
Statistical entropy of a Schwarzschild black hole
Alexanian, M. (1985) · Journal of Statistical Physics · doi:10.1007/bf01009029 · Cited by 2
Entropy radiated by a braneworld black hole
Barrau, A., Grain, J., & Weydert, C. (2007) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.76.087503 · Cited by 3
An Investigation of the Entropy Associated with a Collapsing Molecular Cloud
Kumssa, G. M. (2025) · Astronomy · doi:10.3390/astronomy4010001 · Cited by 1
Flat-space quantum gravity in the AdS/CFT correspondence
Yasunori Nomura, A., Sanches, F., & Weinberg, S. J. (2016) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.93.064049 · Cited by 1
Hawking radiation of some black holes via the non-equilibrium Landauer transport model
Zeng, X.-X., & Liu, W. (2012) · General Relativity and Gravitation · doi:10.1007/s10714-012-1359-y · Cited by 2
Black Hole Entropy from Entropy of Hawking Radiation
Aghapour, S., & Hajian, K. (2016) · Journal of Modern Physics · doi:10.4236/jmp.2016.715181 · Cited by 1
Disentanglement and Black Holes: Information Problem
Radosz, A., Gusin, P., & Roszak, K. (2017) · Acta Physica Polonica A · doi:10.12693/aphyspola.132.132 · Cited by 1
Natural broadening in the quantum emission spectra of higher-dimensional Schwarzschild black holes
Hod, S. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.95.024012 · Cited by 1
The Hawking paradox and the Bekenstein resolution in higher-dimensional spacetimes
Hod, S. (2018) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2018.06.011 · Cited by 1
Upper bound on the energies of the emitted Hawking quanta
Hod, S. (2019) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2019.03.009 · Cited by 1
Thermodynamical fluctuations of massive black holes
Pavón, D., & Rubı́, J. M. (2005) · Springer eBooks · doi:10.1007/bfb0012601 · Cited by 1
Das Informationsproblem bei Schwarzen Löchern
Kiefer, C. (1996) · Physikalische Blätter · doi:10.1002/phbl.19960520411 · Cited by 1
Black Holes in String Theory : Guides to Quantum Gravity
Puhm, A. (2013) · OpenGrey (Institut de l'Information Scientifique et Technique) · Cited by 1
Some remarks on black hole thermodynamicsPreprint
Chiao, R. Y. (2010) · arXiv (Cornell University) · doi:10.48550/arxiv.1012.5657
Radosz, A., Augousti, A. T., & Gusin, P. (2018) · InTech eBooks · doi:10.5772/intechopen.77963
Ziaeepour, H. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2109.05757
Dashtianeh, H., & Sadeghi, J. (2024) · International Journal of Modern Physics A · doi:10.1142/s0217751x24501707
Lowe, D. A., & Lárus Thorlacius, A. (2024) · Journal of High Energy Physics · doi:10.1007/jhep12(2024)033
Information Storage in a Black Hole’s Gravitational Field
He, D., Li, J., & Qiu, Q. (2025) · Entropy · doi:10.3390/e27080870
Melia, F. (2026) · Elsevier eBooks · doi:10.1016/b978-0-44-345201-7.00007-1
Melia, F. (2026) · Elsevier eBooks · doi:10.1016/b978-0-44-345201-7.00010-1
Metadata
- Authors
- Zurek, W. H.
- Affiliations
- California Institute of Technology (US)
- Corresponding author
- Zurek, W. H.
- ORCID
- Zurek, W. H.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1982-12-06
- Volume
- 49
- Issue
- 23
- Pages
- 1683-1686
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W2053923400
- Cited by
- 124
- References
- 13
- Citations by year
- 2026: 2 · 2025: 5 · 2024: 5 · 2023: 5 · 2022: 6 · 2021: 4 · 2020: 4 · 2019: 5 · 2018: 3 · 2017: 4 · 2016: 9 · 2015: 6 · 2014: 7 · 2013: 12 · 2012: 4
- FWCI
- 2.41
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review Letters (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Astrophysical Phenomena and Observations
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Electrodynamics and Casimir Effect
- Keywords
- black hole entropy, black hole evaporation, Hawking radiation, entropy loss, generalized second law of thermodynamics, black hole thermodynamics
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