A General Framework for Linking Free and Forced Fluctuations via Koopmanism
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916802268758016 |
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| author | Lucarini, Valerio Gutierrez, Manuel Santos Moroney, John Zagli, Niccolò |
| author_facet | Lucarini, Valerio Gutierrez, Manuel Santos Moroney, John Zagli, Niccolò |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_16446 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A General Framework for Linking Free and Forced Fluctuations via Koopmanism Lucarini, Valerio Gutierrez, Manuel Santos Moroney, John Zagli, Niccolò Statistical Mechanics Chaotic Dynamics Data Analysis, Statistics and Probability 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. |
| title | A General Framework for Linking Free and Forced Fluctuations via Koopmanism |
| topic | Statistical Mechanics Chaotic Dynamics Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2506.16446 |