{
  "annotation_id": "a0a266c5-fd3b-4f7a-88b2-78919acd3b9e",
  "date_created": "2026-03-02T18:00:46.029000Z",
  "date_modified": "2026-03-02T18:00:46.029000Z",
  "file_hash": "f2bde5b3c20abc08bd6bfd071fa8b4a04865999bfec468d7dfaa9ba8f3f8a78e",
  "private": false,
  "record": {
    "abstract": "Paradoxes in the Boltzmann kinetic theory are presented. Firstly, it is\npointed out that the usual notion concerning the perfect continuity of\ndistribution function is not generally valid; in many important situations\nusing certain types of discontinuous distribution functions is an absolute\nmust. Secondly, it is revealed that there is no time reversibility in terms of\nbeam-to-beam collisions and, in connection with this, there are intrinsic\ndifficulties in formulating the net change of molecular density due to\ncollisions, either in the three-dimensional velocity space or in the\nsix-dimensional phase space. With help of simple examples, the paradoxes\nmanifest themselves clearly.",
    "arxiv_id": "physics/0312043",
    "authors": [
      "C. Y. Chen"
    ],
    "categories": [
      "physics.class-ph",
      "physics.flu-dyn"
    ],
    "title": "Paradoxes in the Boltzmann kinetic theory",
    "url": "https://arxiv.org/abs/physics/0312043"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "88b116b9-0ab0-4d2f-9742-fd88e2d7e014",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}