Anomalous sensitivity to initial conditions and entropy production in standard maps: Nonextensive approach

TL;DR

This paper investigates the complex behavior of coupled standard maps near regularity, demonstrating that nonextensive entropy formalism effectively captures the weak-chaotic dynamics and their relation to sensitivity and entropy production.

Contribution

It introduces a nonextensive approach to analyze sensitivity and entropy in coupled standard maps, especially in weak-chaotic regimes close to regularity.

Findings

Weak-chaotic regions exhibit zero Lyapunov exponents.

Nonextensive formalism captures power-law sensitivity.

Relation between sensitivity and entropy production is characterized.

Abstract

We perform a throughout numerical study of the average sensitivity to initial conditions and entropy production for two symplectically coupled standard maps focusing on the control-parameter region close to regularity. Although the system is ultimately strongly chaotic (positive Lyapunov exponents), it first stays lengthily in weak-chaotic regions (zero Lyapunov exponents). We argue that the nonextensive generalization of the classical formalism is an adequate tool in order to get nontrivial information about this complex phenomenon. Within this context we analyze the relation between the power-law sensitivity to initial conditions and the entropy production.