{
  "id": "1709.01398",
  "version": "v1",
  "published": "2017-09-02T12:05:57.000Z",
  "updated": "2017-09-02T12:05:57.000Z",
  "title": "Hamilton-Jacobi theory for Hamiltonian and non-Hamiltonian systems",
  "authors": [
    "Sergey A. Rashkovskiy"
  ],
  "comment": "27 pages",
  "categories": [
    "quant-ph"
  ],
  "abstract": "A generalization of the Hamilton-Jacobi theory to arbitrary dynamical systems, including non-Hamiltonian ones, is considered. The generalized Hamilton-Jacobi theory is constructed as a theory of ensemble of identical systems moving in the configuration space and described by the continual equation of motion and the continuity equation. For Hamiltonian systems, the usual Hamilton-Jacobi equations naturally follow from this theory. The proposed formulation of the Hamilton-Jacobi theory, as the theory of ensemble, allows interpreting in a natural way the transition from quantum mechanics in the Schrodinger's form to classical mechanics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-02T12:05:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-hamiltonian systems",
      "usual hamilton-jacobi equations",
      "arbitrary dynamical systems",
      "continual equation",
      "generalized hamilton-jacobi theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}