Non-Ergodic Complexity Management

TL;DR

This paper extends the theory of complexity management to non-ergodic systems, demonstrating how single time series can be used to understand their insensitivity to perturbations, which is crucial for real-world applications.

Contribution

It provides a new proof for non-ergodic complexity management using time averages, enabling practical analysis of complex systems without ensemble data.

Findings

Extended the proof of complexity management to non-ergodic systems using time averages.

Showed that single time series can reveal system insensitivity to perturbations.

Validated the approach for real-world complex systems.

Abstract

Linear response theory, the backbone of non-equilibrium statistical physics, has recently been extended to explain how and why non-ergodic renewal processes are insensitive to simple perturbations, such as in habituation. It was established that a permanent correlation resulted between an external stimulus and the response of a complex system generating non-ergodic renewal processes, when the stimulus is a similar non-ergodic process. This is the principle of complexity management, whose proof relies on ensemble distribution functions. Herein we extend the proof to the non-ergodic case using time averages and a single time series, hence making it usable in real life situations where ensemble averages cannot be performed because of the very nature of the complex systems being studied.