Bekenstein bound

It is an upper limit on the thermodynamic entropy \(S\), or Shannon entropy \(H\), that can be contained in a finite region of space which has a finite amount of energy. Or conversely, the maximum amount of information required to perfectly describe a system down to the quantum level.

It implies that the information of a physical system, or the information necessary to perfectly describe that system must be finite if the region of space and energy are finite.

In computer science, this implies that non-finite models such as Turning machines are not realizable as finite devices.

A proof using QFT was given in 2008.

Examples

• According to Bekenstein bound, the entropy of a black hole is proportional to the number of Planck areas that it would take to cover the black hole's event horizon.