What entropy at the edge of chaos?

TL;DR

This paper investigates the applicability of generalized entropy and exponential functions at the edge of chaos, demonstrating their effectiveness through numerical experiments on the logistic map.

Contribution

It extends the conjecture that generalized entropies are valid at the edge of chaos by testing a broad class of deformed entropies and exponentials.

Findings

Entropy increases linearly at the edge of chaos

Sensitivity to initial conditions grows as a generalized exponential

Broader validity of generalized entropies confirmed across various deformed functions

Abstract

Numerical experiments support the interesting conjecture that statistical methods be applicable not only to fully-chaotic systems, but also at the edge of chaos by using Tsallis' generalizations of the standard exponential and entropy. In particular, the entropy increases linearly and the sensitivity to initial conditions grows as a generalized exponential. We show that this conjecture has actually a broader validity by using a large class of deformed entropies and exponentials and the logistic map as test cases.