{
  "annotation_id": "5e773c1a-7e2d-4b91-bbd8-fff364f348db",
  "date_created": "2026-03-02T18:00:57.273000Z",
  "date_modified": "2026-03-02T18:00:57.273000Z",
  "file_hash": "d154134a5da2a4f8549fb71575f5833ab4612dd841833e86a6c4e006243dd26d",
  "private": false,
  "record": {
    "abstract": "In 2001 Astumian published a very simple game which can be described by a\nMarkov chain with absorbing initial and final states. In August 2004 Piotrowski\nand Sladowski asserted that Astumian\u0027s analysis was flawed. However, as was\nshown by Astumian, this statement was wrong. In this comment the properties of\nMarkov chains corresponding to games that are more general than that studied by\nAstumian, are investigated.",
    "arxiv_id": "physics/0412162",
    "authors": [
      "L. Pal"
    ],
    "categories": [
      "physics.data-an",
      "physics.gen-ph"
    ],
    "title": "Late comment on Astumian\u0027s paradox",
    "url": "https://arxiv.org/abs/physics/0412162"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "20564a02-c0b8-489f-b044-067a84e9eaad",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}