A general framework for linking free and forced fluctuations via Koopmanism

Valerio Lucarini, Manuel Santos Gutiérrez, John Moroney and Niccolò Zagli

Chaos, Solitons & Fractals, 2026, vol. 202, issue P1

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 Green functions, which are written as a sum of exponentially decaying terms, each associated one-to-one with a mode of natural variability of the system. Ultraslow decay of the Green functions, or, equivalently, of correlation functions between generic observables indicate proximity to critical behaviour. 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. The success of our approach when combined with strategies like Markov state modelling or kernel extended dynamical mode decomposition is encouraging in terms of advancing the scope of data-driven analysis of response and criticality in high-dimensional systems.

Keywords: Response theory; Fluctuation–dissipation theory; Lorenz ’63 model; Stochastic forcing; Koopman analysis; Ulam method; Markov state modelling; Extended dynamical model decompositions; Kernel methods; Data-driven methods (search for similar items in EconPapers)
Date: 2026
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S096007792501553X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:202:y:2026:i:p1:s096007792501553x

DOI: 10.1016/j.chaos.2025.117540

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().