Broken ergodicity and glassy behavior in a deterministic chaotic map

TL;DR

This paper investigates a deterministic coupled map network revealing broken ergodicity and glassy behavior, with multiple macroscopic states and non-self-averaging properties across chaotic and regular regimes.

Contribution

It demonstrates the existence of a parameter range with numerous macroscopic configurations and violation of self-averaging in a deterministic chaotic network.

Findings

Multiple macroscopic configurations exist in certain parameter ranges.

Time averages do not converge to a single value even as T and N increase.

Broken ergodicity occurs in both chaotic and regular dynamics.

Abstract

A network of $N$ elements is studied in terms of a deterministic globally coupled map which can be chaotic. There exists a range of values for the parameters of the map where the number of different macroscopic configurations is very large, and there is violation of selfaveraging. The time averages of functions, which depend on a single element, computed over a time $T$, have probability distributions that do not collapse to a delta function, for increasing $T$ and $N$. This happens for both chaotic and regular motion, i.e. positive or negative Lyapunov exponent.