{
  "id": "2506.16446",
  "version": "v1",
  "published": "2025-06-19T16:27:30.000Z",
  "updated": "2025-06-19T16:27:30.000Z",
  "title": "A General Framework for Linking Free and Forced Fluctuations via Koopmanism",
  "authors": [
    "Valerio Lucarini",
    "Manuel Santos Gutierrez",
    "John Moroney",
    "Niccolò Zagli"
  ],
  "comment": "18 pages, 3 figures",
  "categories": [
    "cond-mat.stat-mech",
    "nlin.CD",
    "physics.data-an"
  ],
  "abstract": "The link between forced and free fluctuations for nonequilibrium systems can be described via a generalized version of the celebrated fluctuation-dissipation theorem. The use of the formalism of the Koopman operator makes it possible to deliver an intepretable form of the response operators written as a sum of exponentially decaying terms, each associated one-to-one with a mode of natural variability of the system. Here we showcase on a stochastically forced version of the celebrated Lorenz '63 model the feasibility and skill of such an approach by considering different Koopman dictionaries, which allows us to treat also seamlessly coarse-graining approaches like the Ulam method. Our findings provide support for the development of response theory-based investigation methods also in an equation-agnostic, data-driven environment.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-06-19T16:27:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "general framework",
      "forced fluctuations",
      "linking free",
      "koopmanism",
      "response operators written"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}