{
  "id": "1206.3353",
  "version": "v1",
  "published": "2012-06-15T00:51:24.000Z",
  "updated": "2012-06-15T00:51:24.000Z",
  "title": "Generalized information entropies depending only on the probability distribution",
  "authors": [
    "O. Obregón",
    "A. Gil-Villegas"
  ],
  "comment": "13 pages, 3 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Systems with a long-term stationary state that possess as a spatio-temporally fluctuation quantity $\\beta$ can be described by a superposition of several statistics, a \"super statistics\". We consider first, the Gamma, log-normal and $F$-distributions of $\\beta$. It is assumed that they depend only on $p_l$, the probability associated with the microscopic configuration of the system. For each of the three $\\beta-$distributions we calculate the Boltzmann factors and show that they coincide for small variance of the fluctuations. For the Gamma distribution it is possible to calculate the entropy in a closed form, depending on $p_l$, and to obtain then an equation relating $p_l$ with $\\beta E_l$. We also propose, as other examples, new entropies close related with the Kaniadakis and two possible Sharma-Mittal entropies. The entropies presented in this work do not depend on a constant parameter $q$ but on $p_l$. For the $p_l$-Gamma distribution and its corresponding $B_{p_l}(E)$ Boltzmann factor and the associated entropy, we show the validity of the saddle-point approximation. We also briefly discuss the generalization of one of the four Khinchin axioms to get this proposed entropy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-06-15T00:51:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.70.Ln",
      "05.90.+m",
      "89.70.Cf"
    ],
    "keywords": [
      "generalized information entropies depending",
      "probability distribution",
      "gamma distribution",
      "boltzmann factor",
      "long-term stationary state"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1103/PhysRevE.88.062146",
      "journal": "Physical Review E",
      "year": 2013,
      "month": "Dec",
      "volume": 88,
      "number": 6,
      "pages": "062146"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013PhRvE..88f2146O"
    }
  }
}