{
  "id": "2103.09909",
  "version": "v1",
  "published": "2021-03-17T21:09:16.000Z",
  "updated": "2021-03-17T21:09:16.000Z",
  "title": "Stochastic Processes and Statistical Mechanics",
  "authors": [
    "Themis Matsoukas"
  ],
  "comment": "8 pages, 4 figures",
  "categories": [
    "cond-mat.stat-mech",
    "math.PR"
  ],
  "abstract": "Statistical thermodynamics delivers the probability distribution of the equilibrium state of matter through the constrained maximization of a special functional, entropy. Its elegance and enormous success have led to numerous attempts to decipher its language and make it available to problems outside physics, but a formal generalization has remained elusive. Here we show how the formalism of thermodynamics can be applied to any stochastic process. We view a stochastic process as a random walk on the event space of a random variable that produces a feasible distribution of states. The set of feasible distributions obeys thermodynamics: the most probable distribution is the canonical distribution, it maximizes the functionals of statistical mechanics, and its parameters satisfy the same Legendre relationships. Thus the formalism of thermodynamics -- no new functionals beyond those already encountered in statistical physics -- is shown to be a stochastic calculus, a universal language of probability distributions and stochastic processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-17T21:09:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic process",
      "statistical mechanics",
      "probability distribution",
      "problems outside physics",
      "feasible distributions obeys thermodynamics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}