What is it about?
This work establishes linear response theory for a broad and fundamental class of systems—mixed jump-diffusion models (including Lévy processes). Our response formulas significantly generalize the fluctuation-dissipation theorem (FDT) to this class of models, building upon and expanding previous formulations in the field. We reveal a remarkable degree of regularity in how these systems respond to structural perturbations, even with respect to changes in the underlying noise law.
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Why is it important?
A new linear response theory including Lévy processes as well as Gaussian noise. Very important for assessing the risk of climate tipping points, may find applications in epidemiology, biology, finance and more.
Perspectives
The framework is foundational, paving the way for advanced fingerprinting—associating changes in observed signal with specific causal mechanisms. The paper provides examples taken from the climate world, but the theory applies robustly to a very large class of complex systems, from biology to engineering.
Mickael Chekroun
Weizmann Institute of Science
Read the Original
This page is a summary of: Kolmogorov modes and linear response of jump-diffusion models, Reports on Progress in Physics, November 2025, Institute of Physics Publishing,
DOI: 10.1088/1361-6633/ae2206.
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