Nonextensive Pesin identity. Exact renormalization group analytical results for the dynamics at the edge of chaos of the logistic map

TL;DR

This paper analytically demonstrates the validity of the q-generalized Pesin identity at the chaos threshold of the logistic map, linking sensitivity to initial conditions and entropy in the framework of nonextensive statistical mechanics.

Contribution

It provides exact renormalization group analytical results confirming the q-Pesin identity at the edge of chaos in the logistic map.

Findings

Analytical proof of the q-Pesin identity at the chaos threshold.

Confirmation of the link between sensitivity and entropy via nonextensive expressions.

Validation of the nonextensive statistical mechanics framework at critical points.

Abstract

We show that the dynamical and entropic properties at the chaos threshold of the logistic map are naturally linked through the nonextensive expressions for the sensitivity to initial conditions and for the entropy. We corroborate analytically, with the use of the Feigenbaum renormalization group(RG) transformation, the equality between the generalized Lyapunov coefficient $\lambda_{q}$ and the rate of entropy production $K_{q}$ given by the nonextensive statistical mechanics. Our results advocate the validity of the $q$-generalized Pesin identity at critical points of one-dimensional nonlinear dissipative maps.