{
  "id": "1303.4211",
  "version": "v2",
  "published": "2013-03-18T11:31:36.000Z",
  "updated": "2013-03-31T02:50:35.000Z",
  "title": "Invertible mappings and the large deviation theory for the $q$-maximum entropy principle",
  "authors": [
    "R. C. Venkatesan",
    "A. Plastino"
  ],
  "comment": "9 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1303.0444. Typographical errors corrected",
  "categories": [
    "cond-mat.stat-mech",
    "cs.IT",
    "math-ph",
    "math.IT",
    "math.MP"
  ],
  "abstract": "The possibility of reconciliation between canonical probability distributions obtained from the $q$-maximum entropy principle with predictions from the law of large numbers when empirical samples are held to the same constraints, is investigated into. Canonical probability distributions are constrained by both: $(i)$ the additive duality of generalized statistics and $(ii)$ normal averages expectations. Necessary conditions to establish such a reconciliation are derived by appealing to a result concerning large deviation properties of conditional measures. The (dual) $q^*$-maximum entropy principle is shown {\\bf not} to adhere to the large deviation theory. However, the necessary conditions are proven to constitute an invertible mapping between: $(i)$ a canonical ensemble satisfying the $q^*$-maximum entropy principle for energy-eigenvalues $\\varepsilon_i^*$, and, $(ii)$ a canonical ensemble satisfying the Shannon-Jaynes maximum entropy theory for energy-eigenvalues $\\varepsilon_i$. Such an invertible mapping is demonstrated to facilitate an \\emph{implicit} reconciliation between the $q^*$-maximum entropy principle and the large deviation theory. Numerical examples for exemplary cases are provided.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-03-31T02:50:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "maximum entropy principle",
      "large deviation theory",
      "invertible mapping",
      "canonical probability distributions",
      "shannon-jaynes maximum entropy theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.4211V"
    }
  }
}