{
  "id": "1707.03526",
  "version": "v1",
  "published": "2017-07-12T03:31:33.000Z",
  "updated": "2017-07-12T03:31:33.000Z",
  "title": "Generalized Ensemble Theory with Non-extensive Statistics",
  "authors": [
    "Ke-Ming Shen",
    "Ben-Wei Zhang",
    "En-Ke Wang"
  ],
  "comment": "14 pages, 2 figures",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP",
    "nucl-th"
  ],
  "abstract": "The non-extensive canonical ensemble theory is reconsidered with the method of Lagrange multipliers by maximizing Tsallis entropy, with the constraint that the normalized term of Tsallis' $q-$average of physical quantities, the sum $\\sum p_j^q$, is independent of the probability $p_i$ for Tsallis parameter $q$. The self-referential problem in the deduced probability and thermal quantities in non-extensive statistics is thus avoided, and thermodynamical relationships are obtained in a consistent and natural way. We also extend the study to the non-extensive grand canonical ensemble theory and obtain the $q$-deformed Bose-Einstein distribution as well as the $q$-deformed Fermi-Dirac distribution. The theory is further applied to the generalized Planck law to demonstrate the distinct behaviors of the various generalized $q$-distribution functions discussed in literature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-12T03:31:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generalized ensemble theory",
      "non-extensive statistics",
      "distribution",
      "tsallis parameter",
      "self-referential problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}