{
  "id": "1403.4299",
  "version": "v3",
  "published": "2014-03-17T22:51:51.000Z",
  "updated": "2014-07-17T22:35:33.000Z",
  "title": "Gibbs, Boltzmann, and negative temperatures",
  "authors": [
    "Daan Frenkel",
    "Patrick B Warren"
  ],
  "comment": "9 pages, 3 figures, RevTeX 4.1 -- conditionally accepted Am J Phys, with minor changes from previous version",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "In a recent paper, Dunkel and Hilbert [Nature Physics 10, 67-72 (2014)] use an entropy definition due to Gibbs to provide a 'consistent thermostatistics' which forbids negative absolute temperatures. Here we argue that the Gibbs entropy fails to satisfy a basic requirement of thermodynamics, namely that when two bodies are in thermal equilibrium, they should be at the same temperature. The entropy definition due to Boltzmann does meet this test, and moreover in the thermodynamic limit can be shown to satisfy Dunkel and Hilbert's consistency criterion. Thus, far from being forbidden, negative temperatures are inevitable, in systems with bounded energy spectra.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-07-17T22:35:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "negative temperatures",
      "entropy definition",
      "hilberts consistency criterion",
      "forbids negative absolute temperatures",
      "gibbs entropy fails"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1119/1.4895828",
      "journal": "American Journal of Physics",
      "year": 2015,
      "month": "Feb",
      "volume": 83,
      "number": 2,
      "pages": 163
    },
    "note": {
      "typesetting": "RevTeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015AmJPh..83..163F"
    }
  }
}