Comment on the Bekenstein bound

Understand

We propose a rigorous derivation of the Bekenstein upper limit for the entropy/information that can be contained by a physical system in a given finite region of space with given finite energy.

• The starting point is the observation that the derivation of such a bound provided by Casini [6] is similar to the description of the black hole incremental free energy that had been given by the first named author [23].
• The approach here is different but close in the spirit to [6].
• Our bound is obtained by operator algebraic methods, in particular Connes' bimodules, Tomita-Takesaki modular theory and Jones' index are essential ingredients inasmuch as the von Neumann algebras in question are typically of type III.