{
  "id": "1107.5231",
  "version": "v1",
  "published": "2011-07-26T14:59:45.000Z",
  "updated": "2011-07-26T14:59:45.000Z",
  "title": "Superstatistics as the statistics of quasi-equilibrium states: Application to fully developed turbulence",
  "authors": [
    "Mohammad Mehrafarin"
  ],
  "comment": "To appear in Phys. Rev. E (2011)",
  "journal": "Phys. Rev. E 84 (2011) 022102",
  "categories": [
    "cond-mat.stat-mech",
    "physics.flu-dyn"
  ],
  "abstract": "In non-equilibrium states, currents are produced by irreversible processes that take a system toward the equilibrium state, where the current vanishes. We demonstrate, in a general setting, that a superstatistics arises when the system relaxes to a (stationary) quasi-equilibrium state instead, where only the \\textit{mean} current vanishes because of fluctuations. In particular, we show that a current with Gaussian white noise takes the system to a unique class of quasi-equilibrium states, where the superstatistics coincides with Tsallis escort $q$-distributions. Considering the fully developed turbulence as an example of such quasi-equilibrium states, we analytically deduce the power-law spectrum of the velocity structure functions, yielding a correction to the log-normal model which removes its shortcomings with regard to the decreasing higher order moments and the Novikov inequality, and obtain exponents that agree well with the experimental data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-07-26T14:59:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.40.-a",
      "05.70.Ln",
      "47.27.eb",
      "47.27.Jv"
    ],
    "keywords": [
      "fully developed turbulence",
      "current vanishes",
      "application",
      "decreasing higher order moments",
      "quasi-equilibrium state"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "doi": "10.1103/PhysRevE.84.022102",
      "year": 2011,
      "month": "Aug",
      "volume": 84,
      "number": 2,
      "pages": "022102"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011PhRvE..84b2102M"
    }
  }
}