{
  "id": "1905.01672",
  "version": "v1",
  "published": "2019-05-05T12:46:12.000Z",
  "updated": "2019-05-05T12:46:12.000Z",
  "title": "Toward a relative q-entropy",
  "authors": [
    "Nikolaos Kalogeropoulos"
  ],
  "comment": "23 pages, No figures, LaTeX2e",
  "categories": [
    "cond-mat.stat-mech",
    "gr-qc",
    "hep-th",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We address the question and related controversy of the formulation of the $q$-entropy, and its relative entropy counterpart, for models described by continuous (non-discrete) sets of variables. We notice that an $L_p$ normalized functional proposed by Lutwak-Yang-Zhang (LYZ), which is essentially a variation of a properly normalized relative R\\'{e}nyi entropy up to a logarithm, has extremal properties that make it an attractive candidate which can be used to construct such a relative $q$-entropy. We comment on the extremizing probability distributions of this LYZ functional, its relation to the escort distributions, a generalized Fisher information and the corresponding Cram\\'{e}r-Rao inequality. We point out potential physical implications of the LYZ entropic functional and of its extremal distributions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-05T12:46:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "relative q-entropy",
      "lyz entropic functional",
      "generalized fisher information",
      "relative entropy counterpart",
      "escort distributions"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}