{
  "id": "2209.12923",
  "version": "v1",
  "published": "2022-09-26T18:01:03.000Z",
  "updated": "2022-09-26T18:01:03.000Z",
  "title": "Heat flow in a periodically forced, thermostatted chain II",
  "authors": [
    "Tomasz Komorowski",
    "Joel L. Lebowitz",
    "Stefano Olla"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We derive a macroscopic heat equation for the temperature of a pinned harmonic chain subject to a periodic force at its right side and in contact with a heat bath at its left side. The microscopic dynamics in the bulk is given by the Hamiltonian equation of motion plus a reversal of the velocity of a particle occurring independently for each particle at exponential times, with rate $\\gamma$. The latter produces a finite heat conductivity. Starting with an initial probability distribution for a chain of $n$ particles we compute the local temperature given by the expected value of the local energy and current. Scaling space and time diffusively yields, in the $n\\to+\\infty$ limit, the heat equation for the macroscopic temperature profile $T(t,u),$ $t>0$, $u \\in [0,1]$. It is to be solved for initial conditions $T(0,u)$ and specified $T(t,0)=T_-$, the temperature of the left heat reservoir and a fixed heat flux $J$, entering the system at $u=1$. $J$ is the work done by the periodic force which is computed explicitly for each $n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-26T18:01:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "heat flow",
      "thermostatted chain",
      "temperature",
      "periodic force",
      "left heat reservoir"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}