{
  "id": "cond-mat/0304251",
  "version": "v2",
  "published": "2003-04-10T22:02:05.000Z",
  "updated": "2003-06-25T18:50:36.000Z",
  "title": "On the (Boltzmann) Entropy of Nonequilibrium Systems",
  "authors": [
    "S. Goldstein",
    "Joel L. Lebowitz"
  ],
  "comment": "31 pages, in Tex, authors' e-mails: oldstein@math.rutgers.edu, lebowitz@math.rutgers.edu",
  "journal": "Physica D193 (2004) 53-66",
  "doi": "10.1016/j.physd.2004.01.008",
  "categories": [
    "cond-mat.stat-mech",
    "astro-ph"
  ],
  "abstract": "Boltzmann defined the entropy of a macroscopic system in a macrostate $M$ as the $\\log$ of the volume of phase space (number of microstates) corresponding to $M$. This agrees with the thermodynamic entropy of Clausius when $M$ specifies the locally conserved quantities of a system in local thermal equilibrium (LTE). Here we discuss Boltzmann's entropy, involving an appropriate choice of macro-variables, for systems not in LTE. We generalize the formulas of Boltzmann for dilute gases and of Resibois for hard sphere fluids and show that for macro-variables satisfying any deterministic autonomous evolution equation arising from the microscopic dynamics the corresponding Boltzmann entropy must satisfy an ${\\cal H}$-theorem.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-06-25T18:50:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonequilibrium systems",
      "hard sphere fluids",
      "local thermal equilibrium",
      "appropriate choice",
      "dilute gases"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 617442
    }
  }
}