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Cited by 2,166Black Holes and Theoretical PhysicsAstrophysical Phenomena and ObservationsAdvanced Thermodynamics and Statistical Mechanics

Generalized second law of thermodynamics in black-hole physics

Bekenstein, Jacob D.·1974·Physical Review D
DOI 10.1103/physrevd.9.3292
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Abstract

In previous work we introduced the concept of black-hole entropy, which we identified with the surface area of the black hole in question expressed in units of the Planck length squared. We suggested that the appropriate generalization of the second law for a region containing a black hole is that the black-hole entropy plus the common entropy in the black-hole exterior never decreases. Here we establish the validity of this law for the infall of an entropy-bearing system into a much larger and more massive generic stationary black hole. To do this we determine a general lower bound for the increase in black-hole entropy, and an upper bound for the entropy of the system, while allowing for quantum effects at each stage. In passing we show that the generalized second law is a statistical law which becomes over-whelmingly probable in the limit of a macroscopic system. We also consider briefly more general situations. Finally, we give two simple examples of predictions made by the generalized second law for black-hole formation processes.

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Authors
Bekenstein, J. D.
Affiliations
The University of Texas at Austin (US)
Corresponding author
Bekenstein, Jacob D.
Venue
Physical Review D
Publisher
American Physical Society (APS)
Published
1974-06-15
Volume
9
Issue
12
Pages
3292-3300
ISSN
0556-2821 (ISSN-L)
DOI
10.1103/physrevd.9.3292
OpenAlex
W2118082065
Cited by
2,166
References
0
Citations by year
2026: 76 · 2025: 147 · 2024: 129 · 2023: 103 · 2022: 105 · 2021: 109 · 2020: 123 · 2019: 94 · 2018: 89 · 2017: 91 · 2016: 83 · 2015: 67 · 2014: 69 · 2013: 57 · 2012: 48
FWCI
5.03
Type
journal article
Language
en
Open access
closed
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (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 › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
Keywords
generalized second law of thermodynamics, black hole entropy, black holes, stationary black holes, quantum effects, statistical mechanics of black holes, black hole formation, entropy bounds

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