Q:

Information Density of Spacetime

How much information is required to completely describe a given volume in spacetime?

A:

There exists a limit on the maximum amount of entropy (or information) that can be contained in a physical system with a given volume and total energy, which is termed as Bekenstein bound. Though the second law of thermodynamics proposes that the entropy of an isolated system grows to a maximum value, this limit fills that knowledge gap. One can view this as an extension of the second law, limiting the growth of entropy beyond a maximum.
If a system of total energy $E$, including rest masses, is
enclosed in a sphere of radius $R$, then the entropy $S$ of the system is bounded by
$$S \leq \lambda RE$$ where $λ > 0$ is a constant (the value $λ = 2π$ is often proposed).
Here is a rigorous derivation using the general mathematical framework concerning quantum information of infinite systems.
References: Comments on Berkenstein bound

