{
  "id": "cond-mat/0005379",
  "version": "v1",
  "published": "2000-05-23T11:51:05.000Z",
  "updated": "2000-05-23T11:51:05.000Z",
  "title": "Weakly Nonextensive Thermostatistics and the Ising Model with Long--range Interactions",
  "authors": [
    "R. Salazar",
    "A. R. Plastino",
    "R. Toral"
  ],
  "comment": "LaTeX file, 20 pages, 7 figures",
  "doi": "10.1007/s100510070108",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We introduce a nonextensive entropic measure $S_{\\chi}$ that grows like $N^{\\chi}$, where $N$ is the size of the system under consideration. This kind of nonextensivity arises in a natural way in some $N$-body systems endowed with long-range interactions described by $r^{-\\alpha}$ interparticle potentials. The power law (weakly nonextensive) behavior exhibited by $S_{\\chi}$ is intermediate between (1) the linear (extensive) regime characterizing the standard Boltzmann-Gibbs entropy and the (2) the exponential law (strongly nonextensive) behavior associated with the Tsallis generalized $q$-entropies. The functional $S_{\\chi} $ is parametrized by the real number $\\chi \\in[1,2]$ in such a way that the standard logarithmic entropy is recovered when $\\chi=1$ >. We study the mathematical properties of the new entropy, showing that the basic requirements for a well behaved entropy functional are verified, i.e., $S_{\\chi}$ possesses the usual properties of positivity, equiprobability, concavity and irreversibility and verifies Khinchin axioms except the one related to additivity since $S_{\\chi}$ is nonextensive. For $1<\\chi<2$, the entropy $S_{\\chi}$ becomes superadditive in the thermodynamic limit. The present formalism is illustrated by a numerical study of the thermodynamic scaling laws of a ferromagnetic Ising model with long-range interactions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-05-23T11:51:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "long-range interactions",
      "weakly nonextensive thermostatistics",
      "verifies khinchin axioms",
      "standard logarithmic entropy",
      "standard boltzmann-gibbs entropy"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}