# Information Density of Spacetime [closed]

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

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• Depends on what's inside the volume. The limit is given by the Bekenstein bound. – psitae Jan 25 at 16:42

## 1 Answer

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