What is the Volume of Information?
Lance, there is in fact a theorem which gives bounds on this. The Margolus-Levitin theorem bounds the rate of computation in terms of energy density. There is a nice trick which can then be played: If the local energy density exceeds a certain limit, a black hole will form causing an event horizon which will essentially prevent you from getting an answer by causally disconnecting that region of space-time from the rest of the universe. Seth Lloyd has a nice paper using this trick to estimate the computational power of the universe (Phys. Rev. Lett. 88, 237901 (2002), arXiv).

You can of course use similar reasoning on any finite region of space-time.