{
  "id": "1702.05523",
  "version": "v1",
  "published": "2017-02-15T22:50:42.000Z",
  "updated": "2017-02-15T22:50:42.000Z",
  "title": "The Vlasov equation and entropy",
  "authors": [
    "E. E. Perepelkin",
    "B. I. Sadovnikov",
    "N. G. Inozemtseva"
  ],
  "comment": "22 pages",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "It is well-known that the expression \\[m\\left\\langle {\\dot{\\vec{v}}} \\right\\rangle =\\vec{F}\\] is used at solving the Vlasov equation. This work shows that in general case \\[m\\left\\langle {\\dot{\\vec{v}}} \\right\\rangle \\ne m\\frac{d}{dt}\\left\\langle {\\vec{v}} \\right\\rangle =\\vec{F}.\\] It is shown that using substitution \\[m\\left\\langle {\\dot{\\vec{v}}} \\right\\rangle =\\vec{F}\\] narrows the class of the Vlasov equation as it corresponds to constant entropy systems. An equation form for the growing and constant entropy has been obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-15T22:50:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "vlasov equation",
      "constant entropy systems",
      "general case",
      "equation form",
      "well-known"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}