Universal glassy dynamics at noise-perturbed onset of chaos. A route to ergodicity breakdown

TL;DR

This paper demonstrates that the transition to chaos in one-dimensional maps exhibits glass-like dynamics, including aging and two-step relaxation, with universal features described by nonextensive statistics and related to ergodicity breakdown.

Contribution

It reveals universal glassy dynamics at chaos onset, linking bifurcation gaps, relaxation, and entropy with nonextensive statistical mechanics.

Findings

Dynamics show two-step relaxation and aging.

Relaxation time relates to entropy similarly to supercooled liquids.

Analytic expressions involve $q$-exponentials and nonextensive statistics.

Abstract

The dynamics of iterates at the transition to chaos in one-dimensional unimodal maps is shown to exhibit the characteristic elements of the glass transition, e.g. two-step relaxation and aging. The properties of the bifurcation gap induced by external noise, including a relationship between relaxation time and entropy, are seen to be comparable to those of a supercooled liquid above a glass transition temperature. Universal time evolution obtained from the Feigenbaum RG transformation is expressed analytically via $q$-exponentials, and interpreted in terms of nonextensive statistics.