{
  "annotation_id": "f06fad60-aede-446a-a03d-f36ad4dd7689",
  "date_created": "2026-03-02T18:00:39.659000Z",
  "date_modified": "2026-03-02T18:00:39.659000Z",
  "file_hash": "0f72fe65f79c46984f22e022994e314aca0b7d5892f4be34c1e461e5221d8a53",
  "private": false,
  "record": {
    "abstract": "Systematic inaccuracy is inherent in any computational estimate of a\nnon-linear average, such as the free energy difference (Delta-F) between two\nstates or systems, because of the availability of only a finite number of data\nvalues, N. In previous work, we outlined the fundamental statistical\ndescription of this ``finite-sampling error.\u0027\u0027 We now give a more complete\npresentation of (i) rigorous general bounds on the free energy and other\nnonlinear averages, which underscore the universality of the phenomenon; (ii)\nasymptotic N-\u003einfinity expansions of the average behavior of the\nfinite-sampling error in Delta-F estimates; (iii) illustrative examples of\nlarge-N behavior, both in free-energy and other calculations; and (iv) the\nuniversal, large-N relation between the average finite-sampling error and the\nfluctuation in the error. An explicit role is played by Levy and Gaussian\nlimiting distributions.",
    "arxiv_id": "physics/0208015",
    "authors": [
      "Daniel M. Zuckerman",
      "Thomas B. Woolf"
    ],
    "categories": [
      "physics.comp-ph",
      "physics.chem-ph",
      "physics.data-an"
    ],
    "title": "Systematic Finite-Sampling Inaccuracy in Free Energy Differences and   Other Nonlinear Quantities",
    "url": "https://arxiv.org/abs/physics/0208015"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8c57054a-b8f6-48bb-8b68-0838837fe7dd",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}