{
  "id": "0906.0243",
  "version": "v1",
  "published": "2009-06-01T09:31:57.000Z",
  "updated": "2009-06-01T09:31:57.000Z",
  "title": "Functions of Mittag-Leffler and Fox: The Pathway Model to Tsallis Statistics and Beck-Cohen Superstatistics",
  "authors": [
    "A. M. Mathai",
    "H. J. Haubold"
  ],
  "comment": "9 pages, TeX",
  "categories": [
    "cond-mat.stat-mech",
    "math.CA"
  ],
  "abstract": "In reaction rate theory, in production-destruction type models and in reaction-diffusion problems when the total derivatives are replaced by fractional derivatives the solutions are obtained in terms of Mittag-Leffler functions and their generalizations. When fractional calculus enters into the picture the solutions of these problems, usually available in terms of generalized hypergeometric functions, switch to Mittag-Leffler functions and their generalizations into Wright functions and subsequently into Fox functions. In this paper, connections are established among generalized Mittag-Leffler functions, Mathai's pathway model, Tsallis statistics, Beck-Cohen superstatistics, and among corresponding entropic measures. The Mittag-Leffler function, for large values of the parameter, approaches a power-law. For values of the parameter close to zero, the Mittag-Leffler function behaves like a stretched exponential. The Mittag-Leffler function is a generalization of the exponential function and represents a deviation from the exponential paradigm whenever it shows up in solution of physical problems. The paper elucidates the relation between analytic representations of the q-exponential function that is fundamental to Tsallis statistics, Mittag-Leffler, Wright, and Fox functions, respectively, utilizing Mellin-Barnes integral representations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-06-01T09:31:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tsallis statistics",
      "beck-cohen superstatistics",
      "fox functions",
      "fractional calculus enters",
      "generalization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.0243M"
    }
  }
}