{
  "id": "cond-mat/0301590",
  "version": "v1",
  "published": "2003-01-30T13:35:51.000Z",
  "updated": "2003-01-30T13:35:51.000Z",
  "title": "Nonextensive statistical mechanics: Some links with astronomical phenomena",
  "authors": [
    "Constantino Tsallis",
    "Domingo Prato",
    "Angel R. Plastino"
  ],
  "comment": "23 pages including one EPS figure. To appear in the Proceedings of the XIth United Nations / European Space Agency Workshop on Basic Space Sciences, Office for Outer Space Affairs / United Nations (Cordoba, 9-13 September 2002), ed. H. Haubold, special issue of Astrophysics and Space Science (Kluwer Academic Publishers, Dordrecht, 2003). It includes a reply to the criticism by M. Nauenberg, cond-mat/0210561 [version 2]",
  "journal": "Astrophys.Space Sci.290:259-274,2004",
  "doi": "10.1023/B:ASTR.0000032528.99179.4f",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "A variety of astronomical phenomena appear to not satisfy the ergodic hypothesis in the relevant stationary state, if any. As such, there is no reason for expecting the applicability of Boltzmann-Gibbs (BG) statistical mechanics. Some of these phenomena appear to follow, instead, nonextensive statistical mechanics. In the same manner that the BG formalism is based on the entropy $S_{BG}=-k \\sum_i p_i \\ln p_i$, the nonextensive one is based on the form $S_q=k(1-\\sum_ip_i^q)/(q-1)$ (with $S_1=S_{BG}$). The stationary states of the former are characterized by an {\\it exponential} dependence on the energy, whereas those of the latter are characterized by an (asymptotic) {\\it power-law}. A brief review of this theory is given here, as well as of some of its applications, such as the solar neutrino problem, polytropic self-gravitating systems, galactic peculiar velocities, cosmic rays and some cosmological aspects. In addition to these, an analogy with the Keplerian elliptic orbits {\\it versus} the Ptolemaic epicycles is developed, where we show that optimizing $S_q$ with a few constraints is equivalent to optimizing $S_{BG}$ with an infinite number of constraints.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-01-30T13:35:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonextensive statistical mechanics",
      "relevant stationary state",
      "galactic peculiar velocities",
      "solar neutrino problem",
      "keplerian elliptic orbits"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Astrophysics and Space Science",
      "year": 2004,
      "month": "Apr",
      "volume": 290,
      "number": 3,
      "pages": 259
    },
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 619831,
      "adsabs": "2004Ap&SS.290..259T"
    }
  }
}