Bekenstein border

The Bekenstein limit , established and named by Jacob Bekenstein , sets an upper limit for the entropy S of a system of finite energy E in a finite volume (sphere with radius R ), and thus its information content

{\ displaystyle S \ leq {\ frac {2 \ pi k _ {\ mathrm {B}} ER} {\ hbar c}},}

in which

k _{B is} the Boltzmann constant
E Energy of the system including rest energies of enclosed particles
R is the radius of the sphere
${\ displaystyle \ hbar}$ the reduced Planck quantum of action
c the speed of light

is.

This relation was generalized by Gerard 't Hooft in order to limit the entropy in a spherical area of space with a certain surface A :

{\ displaystyle S \ leq {\ frac {k _ {\ mathrm {B}} Ac ^ {3}} {4G \ hbar}}}

where G is the gravitational constant .

The upper limit is precisely the entropy contained in a black hole of this size ( Bekenstein-Hawking entropy ). Since the surface area A of a black hole is proportional to the square of its mass, the upper limit of the amount of information that can be contained in a sphere is also proportional to the square of the mass it contains.

It is unclear whether these limits also apply if one takes the volume of the entire universe as the volume . The holographic principle assumes that this is the case. The problem is generally related to how to correctly define the area bounding the volume in general relativity. In 1999, Raphael Bousso formulated a covariant version of the Bekenstein limit, called the covariant entropy limit or holographic limit by Bousso . It was applicable not only to black hole event horizons, but also to rapidly expanding or collapsing surfaces that cannot be transformed into event horizons.

literature

JD Bekenstein: A universal upper bound on the entropy to energy ratio for bounded systems . In: Physical Review D , 23/1981, pp. 287-298, Abstract doi: 10.1103 / PhysRevD.23.287 .
Bekenstein: How does the entropy-information bound work? In: Foundations of Physics , Volume 35, 2005, pp. 1805-1823, arxiv : quant-ph / 0404042
JD Bekenstein: Generalized second law of thermodynamics in black hole physics . In: Physical Review D , September 15, 1974, pp. 3292-3300; phys.huji.ac.il (PDF; 1.7 MB)

Web links

Bekenstein: Bekenstein bound . Scholarpedia

Individual evidence

↑ Bousso: A Covariant Entropy Conjecture . In: Journal of High Energy Physics , 7, 1999, p. 004, arxiv : hep-th / 9905177
↑ Bousso, Casini, Fisher, Maldacena: Proof of a Quantum Bousso Bound . In: Physical Review D, 90, 2014, arxiv : 1404.5635v2

[1] Bousso: A Covariant Entropy Conjecture . In: Journal of High Energy Physics , 7, 1999, p. 004, arxiv : hep-th / 9905177

[2] Bousso, Casini, Fisher, Maldacena: Proof of a Quantum Bousso Bound . In: Physical Review D, 90, 2014, arxiv : 1404.5635v2