{
  "id": "1509.07369",
  "version": "v1",
  "published": "2015-09-24T13:39:36.000Z",
  "updated": "2015-09-24T13:39:36.000Z",
  "title": "Consistent description of fluctuations requires negative temperatures",
  "authors": [
    "Luca Cerino",
    "Andrea Puglisi",
    "Angelo Vulpiani"
  ],
  "comment": "12 pages, 5 figures, accepted for publication in Journal of Statistical Mechanics: theory and experiment",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We review two definitions of temperature in statistical mechanics, $T_B$ and $T_G$, corresponding to two possible definitions of entropy, $S_B$ and $S_G$, known as surface and volume entropy respectively. We restrict our attention to a class of systems with bounded energy and such that the second derivative of $S_B$ with respect to energy is always negative: the second request is quite natural and holds in systems of obvious relevance, i.e. with a number $N$ of degrees of freedom sufficiently large (examples are shown where $N \\sim 100$ is sufficient) and without long-range interactions. We first discuss the basic role of $T_B$, even when negative, as the parameter describing fluctuations of observables in a sub-system. Then, we focus on how $T_B$ can be measured dynamically, i.e. averaging over a single long experimental trajectory. On the contrary, the same approach cannot be used in a generic system for $T_G$, since the equipartition theorem may be spoiled by boundary effects due to the limited energy. These general results are substantiated by the numerical study of a Hamiltonian model of interacting rotators with bounded kinetic energy. The numerical results confirm that the kind of configurational order realized in the regions at small $S_B$, or equivalently at small $|T_B|$, depends on the sign of $T_B$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-24T13:39:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "consistent description",
      "negative temperatures",
      "fluctuations",
      "single long experimental trajectory",
      "definitions"
    ],
    "publication": {
      "doi": "10.1088/1742-5468/2015/12/P12002",
      "journal": "Journal of Statistical Mechanics: Theory and Experiment",
      "year": 2015,
      "month": "Dec",
      "volume": 2015,
      "number": 12,
      "pages": 12002
    },
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015JSMTE..12..002C"
    }
  }
}