{
  "id": "cond-mat/0303156",
  "version": "v1",
  "published": "2003-03-09T15:12:52.000Z",
  "updated": "2003-03-09T15:12:52.000Z",
  "title": "Extending the definition of entropy to nonequilibrium steady states",
  "authors": [
    "David Ruelle"
  ],
  "comment": "plain TeX, 10 pagesemacs dede",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We study the nonequilibrium statistical mechanics of a finite classical system subjected to nongradient forces $\\xi$ and maintained at fixed kinetic energy (Hoover-Evans isokinetic thermostat). We assume that the microscopic dynamics is sufficiently chaotic (Gallavotti-Cohen chaotic hypothesis) and that there is a natural nonequilibrium steady state $\\rho_\\xi$. When $\\xi$ is replaced by $\\xi+\\delta\\xi$ one can compute the change $\\delta\\rho$ of $\\rho_\\xi$ (linear response) and define an entropy change $\\delta S$ based on energy considerations. When $\\xi$ is varied around a loop, the total change of $S$ need not vanish: outside of equilibrium the entropy has curvature. But at equilibrium (i.e. if $\\xi$ is a gradient) we show that the curvature is zero, and that the entropy $S(\\xi+\\delta\\xi)$ near equilibrium is well defined to second order in $\\delta\\xi$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-03-09T15:12:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "definition",
      "natural nonequilibrium steady state",
      "gallavotti-cohen chaotic hypothesis",
      "hoover-evans isokinetic thermostat",
      "nonequilibrium statistical mechanics"
    ],
    "note": {
      "typesetting": "Plain TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003cond.mat..3156R"
    }
  }
}