{
  "annotation_id": "e63acd7a-08ce-4533-bb68-e346c84790f0",
  "date_created": "2026-03-02T18:02:06.496000Z",
  "date_modified": "2026-03-02T18:02:06.496000Z",
  "file_hash": "d1de72a20da9164e5ec021a45a6e7f856025fae826dc0e8c0fe5e81b3bc7721e",
  "private": false,
  "record": {
    "abstract": "We study the origin of the Born probability rule rho = |psi|^2 in the de\nBroglie-Bohm pilot-wave formulation of quantum theory. It is argued that\nquantum probabilities arise dynamically, and have a status similar to thermal\nprobabilities in ordinary statistical mechanics. This is illustrated by\nnumerical simulations for a two-dimensional system. We show that a simple\ninitial ensemble with a non-standard distribution rho not= |psi|^2 of particle\npositions evolves towards the quantum distribution to high accuracy. The\nrelaxation process rho --\u003e |psi|^2 is quantified in terms of a coarse-grained\nH-function (equal to minus the relative entropy of rho with respect to\n|psi|^2), which is found to decrease approximately exponentially over time,\nwith a time constant that accords with a simple theoretical estimate.",
    "arxiv_id": "quant-ph/0403034",
    "authors": [
      "Antony Valentini",
      "Hans Westman"
    ],
    "categories": [
      "quant-ph",
      "gr-qc",
      "hep-th"
    ],
    "doi": "10.1098/rspa.2004.1394",
    "journal_ref": "Proc.Roy.Soc.Lond.A461:253-272,2005",
    "title": "Dynamical Origin of Quantum Probabilities",
    "url": "https://arxiv.org/abs/quant-ph/0403034"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e918512a-f0ca-408a-8166-7ac5031999ed",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}