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arXiv · 2506.16446

A General Framework for Linking Free and Forced Fluctuations via Koopmanism

Valerio Lucarini·Manuel Santos Gutierrez·John Moroney·Niccolò Zagli
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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.

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Valerio Lucarini, Manuel Santos Gutierrez, John Moroney, Niccolò Zagli. 2025-06-19. A General Framework for Linking Free and Forced Fluctuations via Koopmanism. https://doi.org/10.1016/j.chaos.2025.117540

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