Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

On the validity of linear response theory in high-dimensional deterministic dynamical systems (1801.09377v4)

Published 29 Jan 2018 in math.DS and nlin.CD

Abstract: This theoretical work considers the following conundrum: linear response theory is successfully used by scientists in numerous fields, but mathematicians have shown that typical low-dimensional dynamical systems violate the theory's assumptions. Here we provide a proof of concept for the validity of linear response theory in high-dimensional deterministic systems for large-scale observables. We introduce an exemplary model in which observables of resolved degrees of freedom are weakly coupled to a large, inhomogeneous collection of unresolved chaotic degrees of freedom. By employing statistical limit laws we give conditions under which such systems obey linear response theory even if all the degrees of freedom individually violate linear response. We corroborate our result with numerical simulations.

Summary

We haven't generated a summary for this paper yet.