{
  "id": "cond-mat/0505107",
  "version": "v1",
  "published": "2005-05-04T15:13:45.000Z",
  "updated": "2005-05-04T15:13:45.000Z",
  "title": "A step beyond Tsallis and Renyi entropies",
  "authors": [
    "Marco Masi"
  ],
  "journal": "Physics Letters A Volume 338, Issues 3-5, 2 May 2005, Pages 217-224",
  "doi": "10.1016/j.physleta.2005.01.094",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Tsallis and R\\'{e}nyi entropy measures are two possible different generalizations of the Boltzmann-Gibbs entropy (or Shannon's information) but are not generalizations of each others. It is however the Sharma-Mittal measure, which was already defined in 1975 (B.D. Sharma, D.P. Mittal, J.Math.Sci \\textbf{10}, 28) and which received attention only recently as an application in statistical mechanics (T.D. Frank & A. Daffertshofer, Physica A \\textbf{285}, 351 & T.D. Frank, A.R. Plastino, Eur. Phys. J., B \\textbf{30}, 543-549) that provides one possible unification. We will show how this generalization that unifies R\\'{e}nyi and Tsallis entropy in a coherent picture naturally comes into being if the q-formalism of generalized logarithm and exponential functions is used, how together with Sharma-Mittal's measure another possible extension emerges which however does not obey a pseudo-additive law and lacks of other properties relevant for a generalized thermostatistics, and how the relation between all these information measures is best understood when described in terms of a particular logarithmic Kolmogorov-Nagumo average.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-05-04T15:13:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "renyi entropies",
      "logarithmic kolmogorov-nagumo average",
      "generalization",
      "coherent picture",
      "shannons information"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}