Aging in a Chaotic System

TL;DR

This paper shows aging behavior in a simple chaotic system, using a deterministic chaotic map that exhibits sub-diffusion, modeled with aging continuous time random walks to describe its long-term diffusion properties.

Contribution

It introduces a minimal chaotic map model that demonstrates aging and sub-diffusion, linking chaos theory with aging phenomena in diffusion processes.

Findings

Demonstrates aging behavior in a chaotic map

Models sub-diffusion with aging continuous time random walks

Provides analytical description of asymptotic diffusion behaviors

Abstract

We demonstrate aging behavior in a simple non-linear system. Our model is a chaotic map which generates deterministically sub-diffusion. Asymptotic behaviors of the diffusion process are described using aging continuous time random walks, introduced previously to model diffusion in glasses.