{
  "annotation_id": "db6c190a-ea1f-49a2-ab82-585e3bad8164",
  "date_created": "2026-03-02T18:00:46.726000Z",
  "date_modified": "2026-03-02T18:00:46.726000Z",
  "file_hash": "385a3507ade32e4b4c3fa244cc890182eebe3d145facd39a56a234f90fdd5f0e",
  "private": false,
  "record": {
    "abstract": "Two approximations are frequently used in statistical physics: the first one,\nwhich we shall name the mean values approximation, is generally (and\nimproperly) named as \"maximum term approximation\". The second is the \"Stirling\napproximation\". In this paper we demonstrate that the error introduced by the\nfirst approximation is exactly compensated by the second approximation in the\ncalculation of mean values of multinomial distributions.",
    "arxiv_id": "physics/0309119",
    "authors": [
      "Conrado Hoffmann"
    ],
    "categories": [
      "physics.gen-ph",
      "physics.ed-ph"
    ],
    "title": "On the Use of Approximations in Statistical Physics",
    "url": "https://arxiv.org/abs/physics/0309119"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "392eb4ed-50a5-4ab9-b6c1-3240a75b7139",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}