{
  "id": "2104.13334",
  "version": "v1",
  "published": "2021-04-27T17:14:35.000Z",
  "updated": "2021-04-27T17:14:35.000Z",
  "title": "Derivation of the Onsager Principle from Large Deviation Theory",
  "authors": [
    "Brian R. La Cour",
    "William C. Schieve"
  ],
  "comment": "25 pages, 3 figures",
  "journal": "Physica A 331, 109 (2004)",
  "doi": "10.1016/j.physa.2003.09.005",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "The Onsager linear relations between macroscopic flows and thermodynamics forces are derived from the point of view of large deviation theory. For a given set of macroscopic variables, we consider the short-time evolution of near-equilibrium fluctuations, represented as the limit of finite-size conditional expectations. The resulting asymptotic conditional expectation is taken to represent the typical macrostate of the system and is used in place of the usual time-averaged macrostate of traditional approaches. By expanding in the short-time, near-equilibrium limit and equating the large deviation rate function with the thermodynamic entropy, a linear relation is obtained between the time rate of change of the macrostate and the conjugate initial macrostate. A Green-Kubo formula for the Onsager matrix is derived and shown to be positive semi-definite, while the Onsager reciprocity relations readily follow from time reversal invariance. Although the initial tendency of a macroscopic variable is to evolve towards equilibrium, we find that this evolution need not be monotonic. The example of an ideal Knundsen gas is considered as an illustration.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-27T17:14:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large deviation theory",
      "onsager principle",
      "large deviation rate function",
      "derivation",
      "onsager reciprocity relations"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}