On the time evolution of the entropic index

TL;DR

This paper extends the Kolmogorov-Sinai entropy to non-extensive systems using Tsallis' framework, proposing a method to detect the entropic index Q and discussing its time dependence.

Contribution

It introduces a non-extensive adaptation of Kolmogorov-Sinai entropy and highlights the time dependence of the entropic index Q.

Findings

The adapted entropy is an average over the invariant distribution.

The entropic index Q > 1 is shown to be time dependent.

A method to detect the genuine entropic index Q is proposed.

Abstract

We adapt the Kolmogorov-Sinai entropy to the non-extensive perspective recently advocated by Tsallis. The resulting expression is an average on the invariant distribution, which should be used to detect the genuine entropic index Q. We argue that the condition Q >1 is time dependent.