{
  "id": "2409.19203",
  "version": "v1",
  "published": "2024-09-28T01:33:22.000Z",
  "updated": "2024-09-28T01:33:22.000Z",
  "title": "Idempotent approach to level-2 variational principles in Thermodynamical Formalism",
  "authors": [
    "A. O. Lopes",
    "J. K. Mengue",
    "E. R. Oliveira"
  ],
  "comment": "27 pages",
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this work we introduce an idempotent pressure to level-2 functions and its associated density entropy. All this is related to idempotent pressure functions which is the natural concept that corresponds to the meaning of probability in the level-2 max-plus context. In this general framework the equilibrium states, maximizing the variational principle, are not unique. We investigate the connections with the general convex pressure introduced recently to level-1 functions by Bi\\'{s}, Carvalho, Mendes and Varandas. Our general setting contemplates the dynamical and not dynamical framework. We also study a characterization of the density entropy in order to get an idempotent pressure invariant by dynamical systems acting on probabilities; this is therefore a level-2 result. We are able to produce idempotent pressure functions at level-2 which are invariant by the dynamics of the pushforward map via a form of Ruelle operator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-28T01:33:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "variational principle",
      "idempotent approach",
      "thermodynamical formalism",
      "density entropy",
      "produce idempotent pressure functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}