{
  "id": "1711.02349",
  "version": "v1",
  "published": "2017-11-07T09:21:24.000Z",
  "updated": "2017-11-07T09:21:24.000Z",
  "title": "About thermometers and temperature",
  "authors": [
    "M. Baldovin",
    "A. Puglisi",
    "A. Sarracino",
    "A. Vulpiani"
  ],
  "comment": "19 pages, 8 figures",
  "journal": "J. Stat. Mech. (2017) 113202",
  "doi": "10.1088/1742-5468/aa933e",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.soft"
  ],
  "abstract": "We discuss a class of mechanical models of thermometers and their minimal requirements to determine the temperature for systems out of the common scope of thermometry. In particular we consider: 1) anharmonic chains with long time of thermalization, such as the Fermi-Pasta-Ulam (FPU) model; 2) systems with long-range interactions where the equivalence of ensembles does not always hold; 3) systems featuring absolute negative temperatures. We show that for all the three classes of systems a mechanical thermometer model can be designed: a temporal average of a suitable mechanical observable of the thermometer is sufficient to get an estimate of the system's temperature. Several interesting lessons are learnt from our numerical study: 1) the long thermalization times in FPU-like systems do not affect the thermometer, which is not coupled to normal modes but to a group of microscopic degrees of freedom; 2) a thermometer coupled to a long-range system measures its microcanonical temperature, even at values of the total energy where its canonical temperature would be very different; 3) a thermometer to read absolute negative temperatures must have a bounded total energy (as the system), otherwise it heavily perturbs the system changing the sign of its temperature. Our study shows that in order to work in a correct way also in \"non standard\" cases, the proper model of thermometer must have a special functional form, e.g. the kinetic part cannot be quadratic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-07T09:21:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "thermometer",
      "total energy",
      "read absolute negative temperatures",
      "long thermalization times",
      "long-range system measures"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "IOP"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}