{
  "id": "cond-mat/0407106",
  "version": "v1",
  "published": "2004-07-05T16:29:54.000Z",
  "updated": "2004-07-05T16:29:54.000Z",
  "title": "Lifetime of small systems controlled by autocatalytic reactions",
  "authors": [
    "L. Pal"
  ],
  "comment": "8 pages, 7 figures",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn"
  ],
  "abstract": "By using the point model of reaction kinetics we have studied the stochastic properties of the lifetime of small systems controlled by autocatalytic reaction A+X -> X+X -> A+X, X -> B. Assuming that a system is living only when the number of autocatalytic particles is larger than zero but smaller than a positive integer N, we have calculated the probability of the lifetime provided that the number of substrate particles A is kept constant by a suitable reservoir, and the end-products B do not take part in the reaction. We have shown that the density function of the lifetime is strongly asymmetric and in certain cases it has a well-defined minimum at the beginning of the process. It has been also proven that the extinction probability of systems of this type is exactly 1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-07-05T16:29:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "small systems",
      "autocatalytic reaction",
      "stochastic properties",
      "autocatalytic particles",
      "reaction kinetics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004cond.mat..7106P"
    }
  }
}