{
  "id": "1411.7123",
  "version": "v2",
  "published": "2014-11-26T07:10:16.000Z",
  "updated": "2015-04-11T05:28:12.000Z",
  "title": "Effects of the Tsallis distribution in the linear sigma model",
  "authors": [
    "Masamichi Ishihara"
  ],
  "comment": "10 pages, 6figures",
  "categories": [
    "hep-ph"
  ],
  "abstract": "The effects of the Tsallis distribution which has two parameters, $q$ and $T$,on physical quantities are studied using the linear sigma model in chiral phase transitions.The parameter $T$ dependences of the condensate and mass for various $q$ are shown, where $T$ is called temperature. The Tsallis distribution approaches the Boltzmann-Gibbs distribution as $q$ approaches $1$. The critical temperature and energy density are described with digamma function, and the $q$ dependences of these quantities and the extension of Stefan-Boltzmann limit of the energy density are shown. The following facts are clarified. The chiral symmetry restoration for $q>1$ occurs at low temperature, compared with the restoration at $q=1$. The sigma mass and pion mass reflect the restoration. The critical temperature decreases monotonically as $q$ increases. The small deviation from the Boltzmann-Gibbs distribution results in the large deviations of physical quantities, especially the energy density. It is displayed from the energetic point of view that the small deviation from the Boltzmann-Gibbs distribution is realized for $q>1$. The physical quantities are affected by the Tsallis distribution even when $|q-1|$ is small.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-26T07:10:16.000Z",
      "abstract": "The effects of the Tsallis distribution which has a parameter $q$ on physical quantities are studied using the linear sigma model in chiral phase transitions. The temperature dependences of the condensate and mass for various $q$ are shown, where the Tsallis distribution approaches the Boltzmann-Gibbs distribution as $q$ approaches $1$. The critical temperature and energy density are described with digamma function, and the $q$ dependences of these quantities and the extension of Stefan-Boltzmann limit of the energy density are shown. The following facts are clarified. The chiral symmetry restoration for $q>1$ occurs at low temperature, compared with the restoration for $q=1$. The sigma mass and pion mass reflect the restoration. The critical temperature decreases monotonically as $q$ increases. The small deviation from the Boltzmann-Gibbs distribution results in the large deviations of physical quantities, especially the energy density. It is displayed from the energetic point of view that the small deviation from the Boltzmann-Gibbs distribution is realized.",
      "comment": "6 pages, 3 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-04-11T05:28:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "25.75.Nq",
      "12.40.-y",
      "11.30.Rd",
      "25.75.-q"
    ],
    "keywords": [
      "linear sigma model",
      "energy density",
      "small deviation",
      "critical temperature",
      "physical quantities"
    ],
    "publication": {
      "doi": "10.1142/S0218301315500858",
      "journal": "International Journal of Modern Physics E",
      "year": 2015,
      "month": "Oct",
      "volume": 24,
      "number": 11,
      "pages": 1550085
    },
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1330309,
      "adsabs": "2015IJMPE..2450085I"
    }
  }
}