{
  "id": "1409.7036",
  "version": "v1",
  "published": "2014-09-24T18:28:53.000Z",
  "updated": "2014-09-24T18:28:53.000Z",
  "title": "Schroedinger vs. Navier-Stokes",
  "authors": [
    "P. Fernandez de Cordoba",
    "J. M. Isidro",
    "J. Vazquez Molina"
  ],
  "comment": "14 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Quantum mechanics has been argued to be a coarse-graining of some underlying deterministic theory. Here we support this view by establishing a map between certain solutions of the Schroedinger equation, and the corresponding solutions of the irrotational Navier-Stokes equation for viscous fluid flow. As a physical model for the fluid itself we propose the quantum probability fluid. It turns out that the (state-dependent) viscosity of this fluid is proportional to Planck's constant, while the volume density of entropy is proportional to Boltzmann's constant. Stationary states have zero viscosity and a vanishing time rate of entropy density. On the other hand, the nonzero viscosity of nonstationary states provides an information-loss mechanism whereby a deterministic theory (a classical fluid governed by the Navier-Stokes equation) gives rise to an emergent theory (a quantum particle governed by the Schroedinger equation).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-24T18:28:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "schroedinger equation",
      "quantum probability fluid",
      "irrotational navier-stokes equation",
      "nonzero viscosity",
      "quantum particle"
    ],
    "publication": {
      "doi": "10.3390/e18010034"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1318905,
      "adsabs": "2014arXiv1409.7036F"
    }
  }
}