{
  "id": "1202.2526",
  "version": "v2",
  "published": "2012-02-12T13:11:08.000Z",
  "updated": "2012-04-10T17:25:07.000Z",
  "title": "Micro-canonical thermodynamics: Why does heat flow from hot to cold",
  "authors": [
    "Hans Henrik Rugh"
  ],
  "comment": "5 pages",
  "categories": [
    "cond-mat.stat-mech",
    "math.DS",
    "nlin.CD"
  ],
  "abstract": "We show how to use a central limit approximation for additive co-cycles to describe non-equilibrium and far from equilibrium thermodynamic behavior. We consider first two weakly coupled Hamiltonian dynamical systems initially at different micro-canonical temperatures. We describe a stochastic model where the energy-transfer between the two systems is considered as a random variable satisfying a central limit approximation. We show that fluctuations in energy observables are linearly related to the heat-transfer (dissipation). As a result, on average, heat flows from hot to cold. We also consider the far from equilibrium situation of a non-Hamiltonian thermostatted system as in Evans et al. {\\em Phys.\\ Rev.\\ Lett.} {\\bf 71}, 2401 (1993). Applying the same central limit approximation we re-derive their relation for the violation of the 2nd law of thermodynamics. We note that time-reversal symmetry is not used in our derivation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-04-10T17:25:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "heat flow",
      "central limit approximation",
      "micro-canonical thermodynamics",
      "coupled hamiltonian dynamical systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.2526R"
    }
  }
}