Fluctuation-Response Relation and modeling in systems with fast and slow dynamics

TL;DR

This paper develops a general Fluctuation-Response Relation framework to connect response to perturbations with spontaneous fluctuations in systems with coupled fast and slow variables, tested on Lorenz-96 and simplified models.

Contribution

It introduces a detailed formulation of the Fluctuation-Response Relation for multiscale systems and explores its implications for modeling slow dynamics with Langevin equations.

Findings

Fast dynamics influence slow dynamics through a quadratic response function.

The method accurately describes the response-fluctuation connection in coupled systems.

Beyond a certain timescale, models can only provide statistical predictions.

Abstract

We show how a general formulation of the Fluctuation-Response Relation is able to describe in detail the connection between response properties to external perturbations and spontaneous fluctuations in systems with fast and slow variables. The method is tested by using the 360-variable Lorenz-96 model, where slow and fast variables are coupled to one another with reciprocal feedback, and a simplified low dimensional system. In the Fluctuation-Response context, the influence of the fast dynamics on the slow dynamics relies in a non trivial behavior of a suitable quadratic response function. This has important consequences for the modeling of the slow dynamics in terms of a Langevin equation: beyond a certain intrinsic time interval even the optimal model can give just statistical prediction.