{
  "id": "1811.09089",
  "version": "v1",
  "published": "2018-11-22T10:31:49.000Z",
  "updated": "2018-11-22T10:31:49.000Z",
  "title": "Rényi and Tsallis entropies: three analytic examples",
  "authors": [
    "O. Olendski"
  ],
  "comment": "9 figures",
  "categories": [
    "quant-ph",
    "cond-mat.mes-hall",
    "math-ph",
    "math.MP",
    "physics.ed-ph"
  ],
  "abstract": "A comparative study of one-dimensional quantum structures which allow analytic expressions for the position and momentum R\\'{e}nyi $R(\\alpha)$ and Tsallis $T(\\alpha)$ entropies, focuses on extracting the most characteristic physical features of these one-parameter functionals. Consideration of the harmonic oscillator reconfirms a special status of the Gaussian distribution: at any parameter $\\alpha$ it converts into the equality both R\\'{e}nyi and Tsallis uncertainty relations removing for the latter an additional requirement $1/2\\leq\\alpha\\leq1$ that is a necessary condition for all other geometries. It is shown that the lowest limit of the semi infinite range of the dimensionless parameter $\\alpha$ where \\emph{momentum} components exist strongly depends on the \\emph{position} potential and/or boundary condition for the \\emph{position} wave function. Asymptotic limits reveal that in either space the entropies $R(\\alpha)$ and $T(\\alpha)$ approach their Shannon counterpart, $\\alpha=1$, along different paths. Similarities and differences between the two entropies and their uncertainty relations are exemplified. Some unsolved problems are pointed at too.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-22T10:31:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tsallis entropies",
      "analytic examples",
      "semi infinite range",
      "tsallis uncertainty relations",
      "asymptotic limits reveal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}