On the choice of coarse variables for dynamics

TL;DR

This paper discusses methods for selecting coarse variables that effectively capture the averaged behavior of fine-scale autonomous systems, enabling approximate autonomous dynamics for practical applications.

Contribution

It introduces two ideas for choosing coarse variables that represent averaged behaviors, facilitating approximate autonomous dynamics in complex systems.

Findings

Proposes two methods for selecting coarse variables.

Demonstrates how coarse variables can approximate fine-scale dynamics.

Provides insights into coarse-graining for autonomous systems.

Abstract

Two ideas for the choice of an adequate set of coarse variables allowing approximate autonomous dynamics for practical applications are presented. The coarse variables are meant to represent averaged behavior of a fine-scale autonomous dynamics.