{
  "id": "2311.14248",
  "version": "v1",
  "published": "2023-11-24T01:57:42.000Z",
  "updated": "2023-11-24T01:57:42.000Z",
  "title": "Statistical ensembles in integrable Hamiltonian systems with almost periodic transitions",
  "authors": [
    "Xinyu Liu",
    "Yong Li"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the long-term average evolution of the random ensemble along integrable Hamiltonian systems with time $T$-periodic transitions. More precisely, for any observable $G$, it is demonstrated that the ensemble under $G$ in long time average converges to that over one time period $T$, and that the probability measure induced by the probability density function describing the ensemble at time $t$ weakly converges to the average of the probability measures over time $T$. And we extend the result to almost periodic cases. The key to the proof is based on the {\\it {Riemann-Lebesgue lemma in time-average form}} generalized in the paper. %This work contributes to the comprehension of the statistical mechanics of Hamiltonian systems subject to disturbances.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-24T01:57:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "integrable hamiltonian systems",
      "periodic transitions",
      "statistical ensembles",
      "long time average converges",
      "probability measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}