2020/07/05 by Hannah Earley, Earley, Hannah
Computer Science · Materials Science · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Brownian motion #Computation #Computer science #Constructive #Dissipation #FOS: Physical sciences #Geometry #Mathematical analysis #Mathematics #Nanocluster Synthesis and Applications #Physics #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #RADIUS #Regular polygon #Scaling #Statistical Mechanics (cond-mat.stat-mech) #Statistical physics #Statistics #Upper and lower bounds #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.2007.03605
published in arXiv (Cornell University) (Cornell University) · 33 pages, 3 figures; improve formatting, update citations, add orcid, add supplemental code link, correct QZE derivation
openalex publication_date 2020/07/05 · arxiv created 2021/11/30 · arxiv updated 2021/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
We analyse the maximum achievable rate of sustained computation for a given\nconvex region of three dimensional space subject to geometric constraints on\npower delivery and heat dissipation. We find a universal upper bound across\nboth quantum and classical systems, scaling as \√(AV) where V is the\nregion volume and A its area. Attaining this bound requires the use of\nreversible computation, else it falls to scaling as A. By specialising our\nanalysis to the case of Brownian classical systems, we also give a\nsemi-constructive proof suggestive of an implementation attaining these bounds\nby means of molecular computers. For regions of astronomical size, general\nrelativistic effects become significant and more restrictive bounds\nproportional to \√(AR) and R are found to apply, where R is its\nradius. It is also shown that inhomogeneity in computational structure is\ngenerally to be avoided. These results are depicted graphically in Figure 1.\n