Engines of Parsimony: Part I; Limits on Computational Rates in Physical Systems [article]

Hannah Earley
2021 arXiv   pre-print
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 √(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
more » ... so 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 √(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.
arXiv:2007.03605v6 fatcat:ym3zjgfht5ddfkrbr7cykynh6i