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A General Framework for Linking Free and Forced Fluctuations via Koopmanism

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arxiv 2506.16446 v1 pith:IOA7SAGT submitted 2025-06-19 cond-mat.stat-mech nlin.CDphysics.data-an

Valerio Lucarini , Manuel Santos Gutierrez , John Moroney , Niccolò Zagli This is my paper · ORCID
classification cond-mat.stat-mechnlin.CDphysics.data-an
keywords forcedcelebratedfluctuationsfreekoopmanresponseversionallows
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Markov matrix perturbations to optimize dynamical and entropy functionals

    math.DS 2025-07 conditional novelty 6.0 of 10

    Linear-response optimization algorithms are derived for entropy, KL divergence, and entropy production on Markov chains, with a drift-reconstruction protocol linking matrix perturbations to vector field forcing.

  2. Interpretable and Equation-Free Response Theory for Complex Systems

    cond-mat.stat-mech 2025-02 conditional novelty 6.0 of 10

    For Markov chains, linear and nonlinear response to time-dependent forcings can be written as sums of exponentials governed by the chain's Koopman eigenvalues, enabling equation-free response prediction.

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