  We analyse the maximum achievable rate of sustained computation for a given
convex region of three dimensional space subject to geometric constraints on
power delivery and heat dissipation. We find a universal upper bound across
both quantum and classical systems, scaling as $\sqrt{AV}$ where $V$ is the
region volume and $A$ its area. Attaining this bound requires the use of
reversible computation, else it falls to scaling as $A$. By specialising our
analysis to the case of Brownian classical systems, we also give a
semi-constructive proof suggestive of an implementation attaining these bounds
by means of molecular computers. For regions of astronomical size, general
relativistic effects become significant and more restrictive bounds
proportional to $\sqrt{AR}$ and $R$ are found to apply, where $R$ is its
radius. It is also shown that inhomogeneity in computational structure is
generally to be avoided. These results are depicted graphically in Figure 1.
