{
  "id": "0707.3153",
  "version": "v1",
  "published": "2007-07-20T21:41:27.000Z",
  "updated": "2007-07-20T21:41:27.000Z",
  "title": "Consequences of the H-Theorem from Nonlinear Fokker-Planck Equations",
  "authors": [
    "Veit Schwammle",
    "Fernando D. Nobre",
    "Evaldo M. F. Curado"
  ],
  "comment": "19 pages, no figures",
  "doi": "10.1103/PhysRevE.76.041123",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "A general type of nonlinear Fokker-Planck equation is derived directly from a master equation, by introducing generalized transition rates. The H-theorem is demonstrated for systems that follow those classes of nonlinear Fokker-Planck equations, in the presence of an external potential. For that, a relation involving terms of Fokker-Planck equations and general entropic forms is proposed. It is shown that, at equilibrium, this relation is equivalent to the maximum-entropy principle. Families of Fokker-Planck equations may be related to a single type of entropy, and so, the correspondence between well-known entropic forms and their associated Fokker-Planck equations is explored. It is shown that the Boltzmann-Gibbs entropy, apart from its connection with the standard -- linear Fokker-Planck equation -- may be also related to a family of nonlinear Fokker-Planck equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-07-20T21:41:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.40.Fb",
      "05.20.-y",
      "05.40.Jc",
      "66.10.Cb"
    ],
    "keywords": [
      "nonlinear fokker-planck equation",
      "consequences",
      "general entropic forms",
      "well-known entropic forms",
      "general type"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "year": 2007,
      "month": "Oct",
      "volume": 76,
      "number": 4,
      "pages": "041123"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007PhRvE..76d1123S"
    }
  }
}