{
  "id": "2206.04414",
  "version": "v1",
  "published": "2022-06-09T11:00:07.000Z",
  "updated": "2022-06-09T11:00:07.000Z",
  "title": "Consistency of the structure of Legendre transform in thermodynamics with the Kolmogorov-Nagumo average",
  "authors": [
    "A. M. Scarfone",
    "H. Matsuzoe",
    "T. Wada"
  ],
  "comment": "15 pages, no figures, Elsart article style",
  "journal": "Phys. Lett. A 380, 2022-3028 (2016)",
  "doi": "10.1016/j.physleta.2016.07.012",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We show the robustness of the structure of Legendre transform in thermodynamics against the replacement of the standard linear average with the Kolmogorov-Nagumo nonlinear average to evaluate the expectation values of the macroscopic physical observables. The consequence of this statement is twofold: 1) the relationships between the expectation values and the corresponding Lagrange multipliers still hold in the present formalism; 2) the universality of the Gibbs equation as well as other thermodynamic relations are unaffected by the structure of the average used in the theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-09T11:00:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "legendre transform",
      "kolmogorov-nagumo average",
      "consistency",
      "expectation values",
      "standard linear average"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}