{
  "id": "cond-mat/0411625",
  "version": "v3",
  "published": "2004-11-25T06:03:00.000Z",
  "updated": "2007-07-24T04:38:31.000Z",
  "title": "Maximum Entropy and the Variational Method in Statistical Mechanics: an Application to Simple Fluids",
  "authors": [
    "Chih-Yuan Tseng",
    "Ariel Caticha"
  ],
  "comment": "5 figures. Additional demonstrations on radial distribution functions and equation of states are added",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We develop the method of Maximum Entropy (ME) as a technique to generate approximations to probability distributions. The central results consist in (a) justifying the use of relative entropy as the uniquely natural criterion to select a \"best\" approximation from within a family of trial distributions, and (b) to quantify the extent to which non-optimal trial distributions are ruled out. The Bogoliuvob variational method is shown to be included as a special case. As an illustration we apply our method to simple fluids. In a first use of the ME method the \"exact\" canonical distribution is approximated by that of a fluid of hard spheres and ME is used to select the optimal value of the hard-sphere diameter. A second, more refined application of the ME method approximates the \"exact\" distribution by a suitably weighed average over different hard-sphere diameters and leads to a considerable improvement in accounting for the soft-core nature of the interatomic potential. As a specific example, the radial distribution function and the equation of state for a Lennard-Jones fluid (Argon) are compared with results from molecular dynamics simulations.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-07-24T04:38:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "maximum entropy",
      "simple fluids",
      "statistical mechanics",
      "application",
      "hard-sphere diameter"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004cond.mat.11625T"
    }
  }
}