{
  "id": "1209.4180",
  "version": "v1",
  "published": "2012-09-19T08:44:35.000Z",
  "updated": "2012-09-19T08:44:35.000Z",
  "title": "Nilpotence in Physics: the case of Tsallis entropy",
  "authors": [
    "Anthony J. Creaco",
    "Nikos Kalogeropoulos"
  ],
  "comment": "4 pages. No figures. Presented by the second author at IC-MSQUARE 2012 (Budapest, Hungary, 3-7 September 2012). To appear in the IC-MSQUARE 2012 Proceedings",
  "journal": "J. Phys. Conf. Ser. 410 (2013) 012148",
  "categories": [
    "math-ph",
    "cond-mat.stat-mech",
    "math.MP"
  ],
  "abstract": "In an attempt to understand the Tsallis entropy composition property, we construct an embedding of the reals into the set of $3\\times 3$ upper triangular matrices with real entries. We explore consequences of this embedding and of the geometry of the ambient $3\\times 3$ Heisenberg group. This approach establishes the polynomial growth of the volume of phase space of systems described by the Tsallis entropy and provides a general framework for understanding Abe's formula in terms of the Pansu derivative between Riemannian spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-19T08:44:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nilpotence",
      "tsallis entropy composition property",
      "upper triangular matrices",
      "understanding abes formula",
      "general framework"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/1742-6596/410/1/012148",
      "journal": "Journal of Physics Conference Series",
      "year": 2013,
      "month": "Feb",
      "volume": 410,
      "number": 1,
      "pages": "012148"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013JPhCS.410a2148C"
    }
  }
}