Bekenstein Bound

The Bekenstein Bound, derived by Jacob Bekenstein, imposes a limit on the entropy, and hence information, that can be contained within a box-shaped volume:

Where S is the contained entropy, E is the energy of the contained matter as measured when the matter is moved to an infinite distance (i.e., accounting for binding force potential energies), and L is the length of the box.

This relation was generalized by Gerard t' Hooft, to impose a limit on the entropy that can be contained within a spherical volume with a given surface area (in Planck units), called the Area Bound:

This is simply the entropy contained within a black hole of the specified size. As a black hole's radius is proportional to its mass, the limit to the entropy (and information) contained within a spherical volume is proportional to the square of the contained mass.

It is unclear whether these limits apply when the volume being considered is the universe itself. The Holographic Principle is derived from the assumption that they do.

References

• J. D. Bekenstein, "Generalized second law of thermodynamics in black hole physics", Phys. Rev. D 9, 3292 (1974)
• J. D. Bekenstein, "A universal upper bound on the entropy to energy ratio for bounded systems", Phys. Rev. D 23, 287 (1981)

External Links

• Home page of Gerard 't Hooft.
• Home page of Jacob Bekenstein.