{
  "annotation_id": "5a326188-1f60-496e-90f9-640b84297820",
  "date_created": "2026-03-02T18:02:45.135000Z",
  "date_modified": "2026-03-02T18:02:45.135000Z",
  "file_hash": "8fcc3b8d995143bef8f4189a76cdfe4dd20c1009cf138acc3f45ebdfbc9d752d",
  "private": false,
  "record": {
    "abstract": "Combination of the Liouville equation with the q-averaged energy $U_q =\n\u003cH\u003e_q$ leads to a microscopic framework for nonextensive q-thermodynamics. The\nresulting von Neumann equation is nonlinear: $i\\dot\\rho=[H,\\rho^q]$. In spite\nof its nonlinearity the dynamics is consistent with linear quantum mechanics of\npure states. The free energy $F_q=U_q-TS_q$ is a stability function for the\ndynamics. This implies that q-equilibrium states are dynamically stable. The\n(microscopic) evolution of $\\rho$ is reversible for any q, but for $q\\neq 1$\nthe corresponding macroscopic dynamics is irreversible.",
    "arxiv_id": "quant-ph/9809061",
    "authors": [
      "Marek Czachor",
      "Jan Naudts"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevE.59.R2497",
    "journal_ref": "Phys.Rev. E59 (1999) 2497",
    "title": "Microscopic Foundation of Nonextensive Statistics",
    "url": "https://arxiv.org/abs/quant-ph/9809061"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "49f0343c-c59c-4b1c-94d5-c5fb54d5d710",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}