{
  "id": "2007.03605",
  "version": "v1",
  "published": "2020-07-05T15:59:55.000Z",
  "updated": "2020-07-05T15:59:55.000Z",
  "title": "Engines of Parsimony: Part I; Limits on Computational Rates in Physical Systems",
  "authors": [
    "William Earley"
  ],
  "comment": "34 pages, 3 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-05T15:59:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "computational rates",
      "physical systems",
      "universal upper bound",
      "dimensional space subject",
      "general relativistic effects"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}