{
  "annotation_id": "96a488fe-c894-4637-9185-c99fa755f67d",
  "date_created": "2026-03-02T18:02:34.538000Z",
  "date_modified": "2026-03-02T18:02:34.538000Z",
  "file_hash": "eaaccad6edd5f7f1d0b749bda2a97f0eef44a955b04fbd9489ae9ab98fd5e1c2",
  "private": false,
  "record": {
    "abstract": "This paper is concerned with the ergodic subspaces of the state spaces of\nisolated quantum systems. We prove a new ergodic theorem for closed quantum\nsystems which shows that the equilibrium state of the system takes the form of\na grand canonical density matrix involving a complete commuting set of\nobservables including the Hamiltonian. The result obtained, which is derived\nfor a generic finite-dimensional quantum system, shows that the equilibrium\nstate arising from unitary evolution is always expressible in the canonical\nform, without the consideration of a system-bath decomposition.",
    "arxiv_id": "quant-ph/0702009",
    "authors": [
      "Dorje C. Brody",
      "Daniel W. Hook",
      "Lane P. Hughston"
    ],
    "categories": [
      "quant-ph",
      "hep-th"
    ],
    "doi": "10.1088/1751-8113/40/26/F01",
    "journal_ref": "J.Phys.A40:F503-F510,2007",
    "title": "Unitarity, ergodicity, and quantum thermodynamics",
    "url": "https://arxiv.org/abs/quant-ph/0702009"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e107f11a-07ee-4e8b-8a78-982983a6a06f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}