{
  "id": "1202.0707",
  "version": "v2",
  "published": "2012-02-03T14:04:28.000Z",
  "updated": "2012-02-06T06:03:46.000Z",
  "title": "Power-law distributions and fluctuation-dissipation relation in the stochastic dynamics of two-variable Langevin equations",
  "authors": [
    "Du Jiulin"
  ],
  "comment": "18 pages,63 references",
  "journal": "J. Stat. Mech.(2012)P02006",
  "doi": "10.1088/1742-5468/2012/02/P02006",
  "categories": [
    "cond-mat.stat-mech",
    "physics.chem-ph",
    "physics.class-ph",
    "physics.plasm-ph",
    "physics.space-ph"
  ],
  "abstract": "We show that the general two-variable Langevin equations with inhomogeneous noise and friction can generate many different forms of power-law distributions. By solving the corresponding stationary Fokker-Planck equation, we can obtain a condition under which these power-law distributions are accurately created in a system away from equilibrium. This condition is an energy-dependent relation between the diffusion coefficient and the friction coefficient and thus it provides a fluctuation-dissipation relation for nonequilibrium systems with power-law distributions. Further, we study the specific forms of the Fokker-Planck equation that correctly leads to such power-law distributions, and then present a possible generalization of Klein-Kramers equation and Smoluchowski equation to a complex system, whose stationary-state solutions are exactly a Tsallis distribution.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-02-06T06:03:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "power-law distributions",
      "fluctuation-dissipation relation",
      "stochastic dynamics",
      "general two-variable langevin equations",
      "corresponding stationary fokker-planck equation"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Statistical Mechanics: Theory and Experiment",
      "year": 2012,
      "month": "Feb",
      "volume": 2012,
      "number": 2,
      "pages": 2006
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012JSMTE..02..006D"
    }
  }
}