{
  "id": "cond-mat/9907412",
  "version": "v4",
  "published": "1999-07-27T08:18:06.000Z",
  "updated": "2000-07-07T15:32:42.000Z",
  "title": "The rate of entropy increase at the edge of chaos",
  "authors": [
    "V. Latora",
    "M. Baranger",
    "A. Rapisarda",
    "C. Tsallis"
  ],
  "comment": "6 pages, Latex, 4 figures included, final version accepted for publication in Physics Letters A",
  "journal": "Phys.Lett. A273 (2000) 97",
  "doi": "10.1016/S0375-9601(00)00484-9",
  "categories": [
    "cond-mat.stat-mech",
    "astro-ph",
    "chao-dyn",
    "comp-gas",
    "hep-th",
    "nlin.CD",
    "nlin.CG",
    "nucl-th"
  ],
  "abstract": "Under certain conditions, the rate of increase of the statistical entropy of a simple, fully chaotic, conservative system is known to be given by a single number, characteristic of this system, the Kolmogorov-Sinai entropy rate. This connection is here generalized to a simple dissipative system, the logistic map, and especially to the chaos threshold of the latter, the edge of chaos. It is found that, in the edge-of-chaos case, the usual Boltzmann-Gibbs-Shannon entropy is not appropriate. Instead, the non-extensive entropy $S_q\\equiv \\frac{1-\\sum_{i=1}^W p_i^q}{q-1}$, must be used. The latter contains a parameter q, the entropic index which must be given a special value $q^*\\ne 1$ (for q=1 one recovers the usual entropy) characteristic of the edge-of-chaos under consideration. The same q^* enters also in the description of the sensitivity to initial conditions, as well as in that of the multifractal spectrum of the attractor.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2000-07-07T15:32:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "entropy increase",
      "usual boltzmann-gibbs-shannon entropy",
      "kolmogorov-sinai entropy rate",
      "initial conditions",
      "usual entropy"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 506399
    }
  }
}