{
  "id": "1505.06861",
  "version": "v1",
  "published": "2015-05-26T09:04:21.000Z",
  "updated": "2015-05-26T09:04:21.000Z",
  "title": "Statistical optimization for passive scalar transport: maximum entropy production vs maximum Kolmogorov-Sinay entropy",
  "authors": [
    "Martin Mihelich",
    "Berengere Dubrulle",
    "Didier Paillard",
    "Davide Faranda"
  ],
  "comment": "Nonlinear Processes in Geophysics (2015)",
  "doi": "10.5194/npg-22-187-2015",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We derive rigorous results on the link between the principle of maximum entropy production and the principle of maximum Kolmogorov-Sinai entropy using a Markov model of the passive scalar diffusion called the Zero Range Process. We show analytically that both the entropy production and the Kolmogorov-Sinai entropy seen as functions of f admit a unique maximum denoted fmaxEP and fmaxKS. The behavior of these two maxima is explored as a function of the system disequilibrium and the system resolution N. The main result of this article is that fmaxEP and fmaxKS have the same Taylor expansion at _rst order in the deviation of equilibrium. We find that fmaxEP hardly depends on N whereas fmaxKS depends strongly on N. In particular, for a fixed difference of potential between the reservoirs, fmaxEP (N) tends towards a non-zero value, while fmaxKS (N) tends to 0 when N goes to infinity. For values of N typical of that adopted by Paltridge and climatologists we show that fmaxEP and fmaxKS coincide even far from equilibrium. Finally, we show that one can find an optimal resolution N_ such that fmaxEP and fmaxKS coincide, at least up to a second order parameter proportional to the non-equilibrium uxes imposed to the boundaries.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-26T09:04:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "maximum entropy production",
      "maximum kolmogorov-sinay entropy",
      "passive scalar transport",
      "statistical optimization",
      "second order parameter proportional"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}