{
  "id": "1807.00873",
  "version": "v1",
  "published": "2018-07-02T20:12:01.000Z",
  "updated": "2018-07-02T20:12:01.000Z",
  "title": "A Geometric Approach to the Concept of Extensivity in Thermodynamics",
  "authors": [
    "M. Á. García-Ariza"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "This paper presents a rigorous treatment of the concept of extensivity in equilibrium thermodynamics from a geometric point of view. This is achieved by endowing the manifold of equilibrium states of a system with a smooth atlas that is compatible with the pseudogroup of transformations on a vector space that preserve the radial vector field. The resulting geometric structure allows for accurate definitions of extensive differential forms and scaling, and the well-known relationship between both is reproduced. This structure is represented by a global vector field that is locally written as a radial one. The submanifolds that are transversal to it are embedded, and locally defined by functions with extensive differential. These submanifolds are a geometric generalization of the space of states of a closed system in equilibrium.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-02T20:12:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "80A05",
      "80A10"
    ],
    "keywords": [
      "geometric approach",
      "extensivity",
      "extensive differential",
      "radial vector field",
      "global vector field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}