{
  "annotation_id": "7064460a-5836-488b-baac-9bdfc30283e1",
  "date_created": "2026-03-02T18:01:35.574000Z",
  "date_modified": "2026-03-02T18:01:35.574000Z",
  "file_hash": "ce80772e508d183dd0a739f08be098500548fc80ceae744760ffff6288e3789a",
  "private": false,
  "record": {
    "abstract": "A recently developed treatment of stochastic processes leads to the\nconstruction of a potential landscape for the dynamical evolution of complex\nsystems. Since the existence of a potential function in generic settings has\nbeen frequently questioned in literature,herewe study several related\ntheoretical issues that lie at core of the construction. We showthat the novel\ntreatment,via a transformation,is closely related to the symplectic structure\nthat is central in many branches of theoretical physics. Using this insight, we\ndemonstrate an invariant under the transformation. We further explicitly\ndemonstrate, in one-dimensional case, the contradistinction among the new\ntreatment to those of Ito and Stratonovich, as well as others.Our results\nstrongly suggest that the method from statistical physics can be useful in\nstudying stochastic, complex systems in general.",
    "arxiv_id": "q-bio/0703044",
    "authors": [
      "P. Ao",
      "C. Kwon",
      "H. Qian"
    ],
    "categories": [
      "q-bio.QM",
      "cond-mat.stat-mech",
      "cs.IT",
      "math.DS",
      "math.IT",
      "nlin.AO",
      "q-bio.MN"
    ],
    "journal_ref": "Complexity 12 (2007) 19-27",
    "title": "On the existence of potential landscape in the evolution of complex   systems",
    "url": "https://arxiv.org/abs/q-bio/0703044"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e8b1af7c-6f2f-4c58-a812-b6dc72d0a378",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}