{
  "id": "cond-mat/0212301",
  "version": "v2",
  "published": "2002-12-12T20:42:05.000Z",
  "updated": "2002-12-12T21:00:16.000Z",
  "title": "Temperature fluctuations and mixtures of equilibrium states in the canonical ensemble",
  "authors": [
    "Hugo Touchette"
  ],
  "comment": "14 pages, 2 figures; contribution to the International Workshop on Interdisciplinary Applications of Ideas from Nonextensive Statistical Mechanics and Thermodynamics, April 8-12, 2002, Santa Fe Institute, Santa Fe, New Mexico, USA",
  "journal": "M. Gell-Mann, C. Tsallis (eds.), Nonextensive Entropy -- Interdisciplinary Applications, Oxford University Press, 2002",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "It has been suggested recently that `$q$-exponential' distributions which form the basis of Tsallis' non-extensive thermostatistical formalism may be viewed as mixtures of exponential (Gibbs) distributions characterized by a fluctuating inverse temperature. In this paper, we revisit this idea in connection with a detailed microscopic calculation of the energy and temperature fluctuations present in a finite vessel of perfect gas thermally coupled to a heat bath. We find that the probability density related to the inverse temperature of the gas has a form similar to a $\\chi^2$ density, and that the `mixed' Gibbs distribution inferred from this density is non-Gibbsian. These findings are compared with those obtained by a number of researchers who worked on mixtures of Gibbsian distributions in the context of velocity difference measurements in turbulent fluids as well as secondaries distributions in nuclear scattering experiments.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-12-12T21:00:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "temperature fluctuations",
      "equilibrium states",
      "canonical ensemble",
      "distribution",
      "inverse temperature"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002cond.mat.12301T"
    }
  }
}