{
  "id": "1007.4307",
  "version": "v1",
  "published": "2010-07-25T08:42:49.000Z",
  "updated": "2010-07-25T08:42:49.000Z",
  "title": "Optimal refrigerator",
  "authors": [
    "Armen E. Allahverdyan",
    "Karen Hovhannisyan",
    "Guenter Mahler"
  ],
  "comment": "12 pages, 3 figures",
  "journal": "Phys. Rev. E 81, 051129 (2010)",
  "categories": [
    "cond-mat.stat-mech",
    "quant-ph"
  ],
  "abstract": "We study a refrigerator model which consists of two $n$-level systems interacting via a pulsed external field. Each system couples to its own thermal bath at temperatures $T_h$ and $T_c$, respectively ($\\theta\\equiv T_c/T_h<1$). The refrigerator functions in two steps: thermally isolated interaction between the systems driven by the external field and isothermal relaxation back to equilibrium. There is a complementarity between the power of heat transfer from the cold bath and the efficiency: the latter nullifies when the former is maximized and {\\it vice versa}. A reasonable compromise is achieved by optimizing the product of the heat-power and efficiency over the Hamiltonian of the two system. The efficiency is then found to be bounded from below by $\\zeta_{\\rm CA}=\\frac{1}{\\sqrt{1-\\theta}}-1$ (an analogue of the Curzon-Ahlborn efficiency), besides being bound from above by the Carnot efficiency $\\zeta_{\\rm C} = \\frac{1}{1-\\theta}-1$. The lower bound is reached in the equilibrium limit $\\theta\\to 1$. The Carnot bound is reached (for a finite power and a finite amount of heat transferred per cycle) for $\\ln n\\gg 1$. If the above maximization is constrained by assuming homogeneous energy spectra for both systems, the efficiency is bounded from above by $\\zeta_{\\rm CA}$ and converges to it for $n\\gg 1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-07-25T08:42:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.70.Ln",
      "05.30.-d",
      "07.20.Mc",
      "84.60.-h"
    ],
    "keywords": [
      "optimal refrigerator",
      "efficiency",
      "heat transfer",
      "refrigerator model",
      "level systems"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "doi": "10.1103/PhysRevE.81.051129",
      "year": 2010,
      "month": "May",
      "volume": 81,
      "number": 5,
      "pages": "051129"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010PhRvE..81e1129A"
    }
  }
}