{
  "id": "1904.04669",
  "version": "v1",
  "published": "2019-04-07T22:39:00.000Z",
  "updated": "2019-04-07T22:39:00.000Z",
  "title": "Coconuts and Islanders: A Statistics-First Guide to the Boltzmann Distribution",
  "authors": [
    "Brian Zhang"
  ],
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "The Boltzmann distribution is one of the key equations of thermal physics and is widely used in machine learning as well. Here I derive a Boltzmann distribution in a simple pedagogical example using only tools from a first-year probability course. The example is called \"coconuts and islanders\" and was taught to me by my father, Shoucheng Zhang (1963 - 2018), to whom these notes are dedicated. By focusing on this simple story, which can be easily simulated on a computer, I aim to provide a more accessible and intuitive presentation of the Boltzmann distribution. Yet I hope this exposition also inspires deep thinking about statistical physics. For instance, I show that the coconuts and islanders story illuminates a connection between the \"fundamental assumption of statistical mechanics\"---all microstates are equally probable---and the statistical property of detailed balance.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-07T22:39:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "boltzmann distribution",
      "statistics-first guide",
      "islanders story illuminates",
      "first-year probability course",
      "thermal physics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}