{
  "annotation_id": "38ed0532-b5cc-42c8-a803-8c6f33c12750",
  "date_created": "2026-03-02T18:02:41.301000Z",
  "date_modified": "2026-03-02T18:02:41.301000Z",
  "file_hash": "1aa26d63ba3c38635766fc1f96d02ad6f8921fc891c14ae704ff1564805096f4",
  "private": false,
  "record": {
    "abstract": "We derive explicit expressions for the volume elements of both the minimal\nand maximal monotone metrics over the (n^{2} - 1)-dimensional convex set of n x\nn density matrices for the cases n = 3 and 4. We make further progress for the\nspecific n = 3 maximal-monotone case, by taking the limit of a certain ratio of\nintegration results, obtained using an orthogonal set of eight coordinates. By\ndoing so, we find remarkably simple marginal probability distributions based on\nthe corresponding volume element, which we then use for thermodynamic purposes.\nWe, thus, find a spin-1 analogue of the Langevin function. In the fully general\nn = 4 situation, however, we are impeded in making similar progress by the\ninability to diagonalize a 3 x 3 Hermitian matrix and thereby obtain an\northogonal set of coordinates to use in the requisite integrations.",
    "arxiv_id": "quant-ph/9802019",
    "authors": [
      "Paul B. Slater"
    ],
    "categories": [
      "quant-ph",
      "cond-mat"
    ],
    "title": "Volume Elements of Monotone Metrics on the n x n Density Matrices as   Densities-of-States for Thermodynamic Purposes. II",
    "url": "https://arxiv.org/abs/quant-ph/9802019"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "71692a26-78e3-483c-a2f0-792009016b90",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}