Entropy production and Pesin-like identity at the onset of chaos

TL;DR

This paper extends the relationship between entropy production and sensitivity to initial conditions, akin to Pesin's identity, to a broader class of deformed entropies at the onset of chaos, using the logistic map.

Contribution

It generalizes the Pesin-like identity to deformed entropies and exponentials, clarifying the conditions under which this relationship holds at the edge of chaos.

Findings

The identity holds for a wide class of deformed entropies.

Finite-entropy growth constrains suitable entropies.

The logistic map serves as an effective test case.

Abstract

Asymptotically entropy of chaotic systems increases linearly and the sensitivity to initial conditions is exponential with time: these two behaviors are related. Such relationship is the analogous of and under specific conditions has been shown to coincide with the Pesin identity. Numerical evidences support the proposal that the statistical formalism can be extended to the edge of chaos by using a specific generalization of the exponential and of the Boltzmann-Gibbs entropy. We extend this picture and a Pesin-like identity to a wide class of deformed entropies and exponentials using the logistic map as a test case. The physical criterion of finite-entropy growth strongly restricts the suitable entropies. The nature and characteristics of this generalization are clarified.