Holographic bound from second law of thermodynamics

Bekenstein, Jacob D.

doi:10.1016/s0370-2693(00)00450-0

Cited by 55 publications

(78 citation statements)

References 15 publications

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“…Thus, we have indeed obtained an upper bound on the entropy of a large class of spacetimes. Notice that this bound tightens the semiclassical Bekenstein bound [13], which is of course expected because of its quantum kinematical underpinning. We now turn to an exposé of this underlying structure within the framework of Quantum Geometry.…”

Section: Holography and The Entropy Boundsupporting

confidence: 52%

Black Hole Entropy: Certain Quantum Features

Majumdar

2002

The Ninth Marcel Grossmann Meeting

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The issue of black hole entropy is reexamined within a finite lattice framework along the lines of Wheeler, 't Hooft and Susskind, with an additional criterion to identify physical horizon states contributing to the entropy. As a consequence, the degeneracy of physical states is lower than that attributed normally to black holes. This results in corrections to the Bekenstein-Hawking area law that are logarithmic in the horizon area. Implications for the holographic entropy bound on bounded spaces are discussed. Theoretical underpinnings of the criterion imposed on the states, based on the 'quantum geometry' formulation of quantum gravity, are briefly explained.

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Section: Holography and The Entropy Boundsupporting

confidence: 52%

Black Hole Entropy: Certain Quantum Features

Majumdar

2002

The Ninth Marcel Grossmann Meeting

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“…The present account leaves out a number of details treated in the original paper. 4 Beyond that one can imagine situations which would sidestep the proof in Sec. 3.…”

Section: Summary and Caveatsmentioning

confidence: 97%

“…Now, it is pretty clear that the area A of a 2-D surface enclosing V must exceed 4π(2E) 2 for otherwise V would already be a black hole (there are pathological surfaces which can be smaller; see Ref. 4 for a cleaner definition). And it must exceed it substantially; otherwise V would be unstable against black hole formation, i.e., not quiescent.…”

Section: Systems With Weak Self-gravitymentioning

confidence: 99%

Holographic Bound From Second Law

Bekenstein¹

2002

The Ninth Marcel Grossmann Meeting

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The holographic bound that the entropy (log of number of quantum states) of a system is bounded from above by a quarter of the area of a circumscribing surface measured in Planck areas is widely regarded a desideratum of any fundamental theory, but some exceptions occur. By suitable black hole gedanken experiments I show that the bound follows from the generalized second law for two broad classes of isolated systems: generic weakly gravitating systems composed of many elementary particles, and quiescent, nonrotating strongly gravitating configurations well above Planck mass. These justify an early claim by Susskind. What is the holographic bound ?The holographic principle, first enunciated by 't Hooft, 1 claims the physical equivalence between pairs of physical theories. One member of a pair, T1, describes a bulk system U in a spacetime; the allied theory, T2, describes a boundary of that spacetime. For instance, string theory in the D = 10 spacetime AdS 5 × S 5 is known to be equivalent to a supersymmetric gauge theory on the boundary. Some more examples are known, mostly in D > 4. Many regard the holographic principle as a criterion for good physics.An obvious consistency requirement on the holographic principle is that the boundary of any system should be able to encode as much information as required to catalogue the quantum states of the bulk system: T2 should allow at least as many quantum states to reside on the boundary as T1 allows for the bulk (otherwise, so to speak, T2 does not know enough to be equivalent to T1). Suppose we go to D = 4 and take the logarithm of this inequality. On the one hand we get the entropy S of U and its gravitational field; on the other we get the entropy of the boundary, which analogy with black hole entropy suggests to quantify by one quarter of its 2-D area A in Planck units. Thus we have the guess (the holographic bound 1,2 here denoted HB; Planck units used throughout !)How do we know that this bound is true ? As support for the HB, Susskind 2 described a gedanken experiment in which a system violating the HB is forced to collapse to a black hole by adding to it extra entropy-free matter. Susskind interprets the ensuing apparent violation of the generalized second law (GSL) as evidence that the envisaged system cannot really exist. In the clearer reformulation of Wald, 3 one imagines the system as a spherically symmetric one of radius R, energy E (with R > 2E, of course) and entropy S which violates the HB: S > πR 2 . A spherically symmetric and concentric shell of mass R/2 − E is dropped on the system; by Birkhoff's theorem the total mass is now R/2. If the outermost surface of the shell reaches Schwarzschild radial coordinate 1

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“…The holographic principle [1][2][3] provides a remarkably simple geometric answer to the following physically interesting question: what is the maximal entropy (information) content of a spatially bounded physical system? In particular, the holographic entropy bound asserts that the remarkably compact inequality [1][2][3][4][5] S ≤ S max ¼ A 4l…”

Section: Introductionmentioning

confidence: 99%

“…In particular, the holographic entropy bound asserts that the remarkably compact inequality [1][2][3][4][5] S ≤ S max ¼ A 4l…”

Section: Introductionmentioning

confidence: 99%

Holographic entropy bound in higher-dimensional spacetimes

Hod¹

2018

Phys. Rev. D

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The celebrated holographic entropy bound asserts that, within the framework of a self-consistent quantum theory of gravity, the maximal entropy (information) content of a physical system is given by one quarter of its circumscribing area: S ≤ S max ¼ A=4l 2 P (here l P is the Planck length). An intriguing possible counterexample to this fundamental entropy bound, which involves homogenous weakly self-gravitating confined thermal fields in higher-dimensional spacetimes, was proposed almost a decade ago. Interestingly, in the present paper we shall prove that this composed physical system, which at first sight seems to violate the holographic entropy bound, actually conforms to the entropy-area inequality S ≤ A=4l 2 P . In particular, we shall explicitly show that the homogeneity property of the confined thermal fields sets an upper bound on the entropy content of the system. The present analysis therefore resolves the apparent violation of the holographic entropy bound by confined thermal fields in higher-dimensional spacetimes.

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Holographic bound from second law of thermodynamics

Cited by 55 publications

References 15 publications

Black Hole Entropy: Certain Quantum Features

Black Hole Entropy: Certain Quantum Features

Holographic Bound From Second Law

Holographic entropy bound in higher-dimensional spacetimes

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