{
  "id": "2105.03191",
  "version": "v1",
  "published": "2021-05-07T11:57:25.000Z",
  "updated": "2021-05-07T11:57:25.000Z",
  "title": "Conditional entropy; an alternative derivation of the pair correlation function for simple classical fluids",
  "authors": [
    "Richard Bonneville"
  ],
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We present an alternative derivation of the pair correlation function for simple classical fluids by using a variational approach. That approach involves the conditional probability p(3,..., N /1, 2) of an undefined system of N particles with respect to a given pair (1,2), and the definition of a conditional entropy $\\sigma$(3,..., N /1, 2). An additivity assumption of $\\sigma$(3,..., N /1, 2) together with a superposition assumption for p(3 / 1, 2) allows deriving the pair probability p(1,2). We then focus onto the case of simple classical fluids, which leads to an integral, non-linear equation that formally allows computing the pair correlation function g(R). That equation admits the one resulting from the hyper netted chain approximation (and the Percus-Yevick approximation) as a limit case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-07T11:57:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "pair correlation function",
      "simple classical fluids",
      "conditional entropy",
      "alternative derivation",
      "hyper netted chain approximation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}