A General Framework for Linking Free and Forced Fluctuations via Koopmanism
arXiv:2506.16446 · doi:10.1016/j.chaos.2025.117540
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.
18 pages, 3 figures
References in corpus (31)
- Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
- A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition
- Fluctuation-Dissipation: Response Theory in Statistical Physics
- Applied Koopmanism
- Equilibrium free energies from non-equilibrium metadynamics
- An update on nonequilibrium linear response
- Forward and Adjoint Sensitivity Computation of Chaotic Dynamical Systems
- Eigendecompositions of Transfer Operators in Reproducing Kernel Hilbert Spaces
- A Statistical Mechanical Approach for the Computation of the Climatic Response to General Forcings
- Predicting Climate Change using Response Theory: Global Averages and Spatial Patterns
- Estimating long term behavior of flows without trajectory integration: the infinitesimal generator approach
- Fluctuations, Response, and Resonances in a Simple Atmospheric Model
- Evidence of dispersion relations for the nonlinear response of the Lorenz 63 system
- Linear response, susceptibility and resonances in chaotic toy models
- Beyond the linear Fluctuation-Dissipation Theorem: the Role of Causality
- On the Fluctuation-Dissipation Relation in non-equilibrium and non-Hamiltonian systems
- Theoretical tools for understanding the climate crisis from Hasselmann's program and beyond
- Response Operators for Markov Processes in a Finite State Space: Radius of Convergence and Link to the Response Theory for Axiom A Systems
- Scalable Extended Dynamic Mode Decomposition using Random Kernel Approximation
- Resonances in a Chaotic Attractor Crisis of the Lorenz Flow
- On Some Aspects of the Response to Stochastic and Deterministic Forcings
- Ruelle-Pollicott Resonances of Stochastic Systems in Reduced State Space. Part I: Theory
- Response and Sensitivity Using Markov Chains
- Nambu representation of an extended Lorenz model with viscous heating
- A kernel-based approach to molecular conformation analysis
- Response Theory and Phase Transitions for the Thermodynamic Limit of Interacting Identical Systems
- Optimal linear responses for Markov chains and stochastically perturbed dynamical systems
- Elements of a unified framework for response formulae
- Detecting and Attributing Change in Climate and Complex Systems: Foundations, Green's Functions, and Nonlinear Fingerprints
- Decomposing the Dynamics of the Lorenz 1963 model using Unstable Periodic Orbits: Averages, Transitions, and Quasi-Invariant Sets
- Similarity signature curves for forming periodic orbits in the Lorenz system