{
  "id": "2005.06289",
  "version": "v1",
  "published": "2020-05-13T12:40:34.000Z",
  "updated": "2020-05-13T12:40:34.000Z",
  "title": "Sustaining a temperature difference",
  "authors": [
    "Matteo Polettini",
    "Alberto Garilli"
  ],
  "comment": "Submission to SciPost",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We derive an expression for the minimal rate of entropy that sustains two reservoirs at different temperatures $T_0$ and $T_\\ell$. The law displays an intuitive $\\ell^{-1}$ dependency on the relative distance and a characterisic $\\log^2 (T_\\ell/T_0)$ dependency on the boundary temperatures. First we give a back-of-envelope argument based on the Fourier Law (FL) of conduction, showing that the least-dissipation profile is exponential. Then we revisit a model of a chain of oscillators, each coupled to a heat reservoir. In the limit of large damping we reobtain the exponential and squared-log behaviors, providing a self-consistent derivation of the FL. For small damping \"equipartition frustration\" leads to a well-known balistic behaviour, whose incompatibility with the FL posed a long-time challenge.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-13T12:40:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "temperature difference",
      "well-known balistic behaviour",
      "exponential",
      "dependency",
      "boundary temperatures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}