{
  "id": "1809.02219",
  "version": "v1",
  "published": "2018-09-06T21:09:07.000Z",
  "updated": "2018-09-06T21:09:07.000Z",
  "title": "Configurational entropy of polydisperse systems can never reach zero",
  "authors": [
    "Vasili Baranau",
    "Ulrich Tallarek"
  ],
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.soft"
  ],
  "abstract": "We present examples of systems whose configurational entropy $S_{\\text{conf}}$ can never reach zero and is instead limited from below by the entropy of mixing $S_{\\text{mix}}$ of the corresponding ideal gas. We use $S_{\\text{conf}}$ defined through the local minima of the potential energy landscape, $S_{\\text{conf}}^{\\text{PEL}}$. We show that this happens in mean-field models, in collections of hard spheres with infinitesimal polydispersity, and for one-dimensional hard rods. We demonstrate that these results match recent advances in understanding the configurational entropy defined in the free energy landscape, $S_{\\text{conf}}^{\\text{FEL}}$. We demonstrate that if $\\min( S_{\\text{conf}}^{\\text{FEL}} ) = 0$, then for an arbitrary system $\\min( S_{\\text{conf}}^{\\text{PEL}} ) = A N + S_{\\text{mix}}$, where $N$ is the number of particles and $A$ is some constant determined by the interaction potential. We discuss which implications these results have on the Adam--Gibbs (AG) and RFOT relations and show that the latter retain a physically meaningful shape for both configurational entropies, $S_{\\text{conf}}^{\\text{FEL}}$ and $S_{\\text{conf}}^{\\text{PEL}}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-06T21:09:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "configurational entropy",
      "reach zero",
      "polydisperse systems",
      "free energy landscape",
      "potential energy landscape"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}