{
  "id": "1507.06479",
  "version": "v1",
  "published": "2015-07-23T12:58:04.000Z",
  "updated": "2015-07-23T12:58:04.000Z",
  "title": "Typicality of thermal equilibrium and thermalization in isolated macroscopic quantum systems",
  "authors": [
    "Hal Tasaki"
  ],
  "comment": "63 pages, 4 figures",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "Based on the view that thermal equilibrium should be characterized through macroscopic observations, we develop a general theory about typicality of thermal equilibrium and the approach to thermal equilibrium in macroscopic quantum systems. We first formulate the notion that a pure state in an isolated quantum system represents thermal equilibrium. Then by assuming, or proving in certain classes of nontrivial models (including that of two bodies in thermal contact), large-deviation type bounds (which we call thermodynamic bounds) for the microcanonical ensemble, we prove that to represent thermal equilibrium is a typical property for pure states in the microcanonical energy shell. We also establish the approach to thermal equilibrium under two different assumptions; one is that the initial state has a moderate energy distribution, and the other is the energy eigenstate thermalization hypothesis. We also discuss three easily solvable models in which these assumptions can be verified.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-23T12:58:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "isolated macroscopic quantum systems",
      "quantum system represents thermal equilibrium",
      "typicality",
      "thermalization",
      "isolated quantum system represents thermal"
    ],
    "publication": {
      "doi": "10.1007/s10955-016-1511-2",
      "journal": "Journal of Statistical Physics",
      "year": 2016,
      "month": "Apr",
      "pages": 76
    },
    "note": {
      "typesetting": "TeX",
      "pages": 63,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016JSP...tmp...76T"
    }
  }
}