{
  "id": "math-ph/0210030",
  "version": "v1",
  "published": "2002-10-15T12:49:38.000Z",
  "updated": "2002-10-15T12:49:38.000Z",
  "title": "The algebraic entropy of classical mechanics",
  "authors": [
    "Robert I McLachlan",
    "Brett Ryland"
  ],
  "comment": "23 pages, 2 figures, submitted to J Math Phys",
  "doi": "10.1063/1.1576904",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We describe the `Lie algebra of classical mechanics', modelled on the Lie algebra generated by kinetic and potential energy of a simple mechanical system with respect to the canonical Poisson bracket. It is a polynomially graded Lie algebra, a class we introduce. We describe these Lie algebras, give an algorithm to calculate the dimensions $c_n$ of the homogeneous subspaces of the Lie algebra of classical mechanics, and determine the value of its entropy $\\lim_{n\\to\\infty} c_n^{1/n}$. It is $1.82542377420108...$, a fundamental constant associated to classical mechanics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-10-15T12:49:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B01",
      "70G45"
    ],
    "keywords": [
      "classical mechanics",
      "algebraic entropy",
      "simple mechanical system",
      "fundamental constant",
      "canonical poisson bracket"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}