Intermittency at critical transitions and aging dynamics at edge of chaos

TL;DR

This paper explores the application of Tsallis statistics to critical transitions and aging dynamics at the edge of chaos, revealing universal behaviors and connections to glass formation in thermal systems.

Contribution

It demonstrates the role of Tsallis statistics and $q$-indices in describing universality classes at bifurcations and links these concepts to glass formation and criticality in thermal systems.

Findings

Tsallis statistics applies at intermittency transitions and Feigenbaum attractors.

Identification of special $q$-values at the edge of chaos.

Connections between unimodal map dynamics and glass formation.

Abstract

We recall that, at both the intermittency transitions and at the Feigenbaum attractor in unimodal maps of non-linearity of order $\zeta >1$, the dynamics rigorously obeys the Tsallis statistics. We account for the $q$-indices and the generalized Lyapunov coefficients $\lambda_{q}$ that characterize the universality classes of the pitchfork and tangent bifurcations. We identify the Mori singularities in the Lyapunov spectrum at the edge of chaos with the appearance of a special value for the entropic index $q$. The physical area of the Tsallis statistics is further probed by considering the dynamics near criticality and glass formation in thermal systems. In both cases a close connection is made with states in unimodal maps with vanishing Lyapunov coefficients.