{
  "id": "1712.02257",
  "version": "v1",
  "published": "2017-12-06T16:16:19.000Z",
  "updated": "2017-12-06T16:16:19.000Z",
  "title": "Extremal flows on Wasserstein space",
  "authors": [
    "Giovanni Conforti",
    "Michele Pavon"
  ],
  "comment": "19 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We develop an intrinsic geometric approach to calculus of variations on Wasserstein space. We show that the flows associated to the Schroedinger bridge with general prior, to Optimal Mass Transport and to the Madelung fluid can all be characterized as annihilating the first variation of a suitable action. We then discuss the implications of this unified framework for stochastic mechanics: It entails, in particular, a sort of fluid-dynamic reconciliation between Bohm's and Nelson's stochastic mechanics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-06T16:16:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "wasserstein space",
      "extremal flows",
      "nelsons stochastic mechanics",
      "intrinsic geometric approach",
      "optimal mass transport"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}