{
  "id": "cond-mat/0110046",
  "version": "v1",
  "published": "2001-10-02T02:01:53.000Z",
  "updated": "2001-10-02T02:01:53.000Z",
  "title": "The additivity of the pseudo-additive conditional entropy for a proper Tsallis' entropic index",
  "authors": [
    "T. Wada",
    "T. Saito"
  ],
  "comment": "LaTeX2e, elsart, 4 pages, no figure, contributed paper to the Proceedings of the International School and Workshop on Nonextensive Thermodynamics and physical applications, NEXT 2001, 23-30 May 2001, Cagliari (Italy) (Physica A)",
  "journal": "Physica A 301 (2001) 284-290",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "For Tsallis' entropic analysis to the time evolutions of standard logistic map at the Feigenbaum critical point, it is known that there exists a unique value $q^*$ of the entropic index such that the asymptotic rate $K_q \\equiv \\lim_{t \\to \\infty} \\{S_q(t)-S_q(0)\\} / t$ of increase in $S_q(t)$ remains finite whereas $K_q$ vanishes (diverges) for $q > q^* (q < q^*)$. We show that in spite of the associated whole time evolution cannot be factorized into a product of independent sub-interval time evolutions, the pseudo-additive conditional entropy $S_q(t|0) \\equiv \\{S_q(t)-S_q(0)\\}/ \\{1+(1-q)S_q(0)\\}$ becomes additive when $q=q^*$. The connection between $K_{q^*}$ and the rate $K'_{q^*} \\equiv S_{q^*}(t | 0) / t$ of increase in the conditional entropy is discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-10-02T02:01:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "pseudo-additive conditional entropy",
      "entropic index",
      "proper tsallis",
      "independent sub-interval time evolutions",
      "additivity"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}