{
  "id": "2402.04214",
  "version": "v1",
  "published": "2024-02-06T18:13:18.000Z",
  "updated": "2024-02-06T18:13:18.000Z",
  "title": "Symmetry shapes thermodynamics of macroscopic quantum systems",
  "authors": [
    "Vasco Cavina",
    "Ariane Soret",
    "Timur Aslyamov",
    "Krzysztof Ptaszyński",
    "Massimiliano Esposito"
  ],
  "comment": "10 pages, 2 figures",
  "categories": [
    "quant-ph",
    "cond-mat.stat-mech"
  ],
  "abstract": "We derive a systematic approach to the thermodynamics of quantum systems based on the underlying symmetry groups. We show that the entropy of a system can be described in terms of group-theoretical quantities that are largely independent of the details of its density matrix. We apply our technique to generic $N$ identical interacting $d$-level quantum systems. Using permutation invariance, we find that, for large $N$, entropy displays a universal large deviation behavior with a rate function $s(\\boldsymbol{x})$ that is completely independent of the microscopic details of the model, but depends only on the size of the irreducible representations of the permutation group $\\text{S}_N$. In turn, the partition function is shown to satisfy a large deviation principle with a free energy $f(\\boldsymbol{x})=e(\\boldsymbol{x})-\\beta^{-1}s(\\boldsymbol{x})$, where $e(\\boldsymbol{x})$ is a rate function that only depends on the ground state energy of particular subspaces determined by group representation theory. We apply our theory to the transverse-field Curie-Weiss model, a minimal model of phase transition exhibiting an interplay of thermal and quantum fluctuations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-02-06T18:13:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "macroscopic quantum systems",
      "symmetry shapes thermodynamics",
      "rate function",
      "universal large deviation behavior",
      "level quantum systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}