Symbolic Sequences and Tsallis Entropy

TL;DR

This paper investigates symbolic sequences with long-range correlations using Tsallis entropy, revealing how correlations affect entropy growth and diffusive behavior depending on sequence parameters.

Contribution

It introduces a computational approach to analyze correlated symbolic sequences and demonstrates the applicability of Tsallis entropy in characterizing their properties.

Findings

Entropy increases more slowly with correlations.

Tsallis entropy shows linear behavior for specific q values.

Sequence diffusion varies with parameter μ.

Abstract

We address this work to investigate symbolic sequences with long-range correlations by using computational simulation. We analyze sequences with two, three and four symbols that could be repeated $l$ times, with the probability distribution $p(l)\propto 1/ l^{\mu}$. For these sequences, we verified that the usual entropy increases more slowly when the symbols are correlated and the Tsallis entropy exhibits, for a suitable choice of $q$, a linear behavior. We also study the chain as a random walk-like process and observe a nonusual diffusive behavior depending on the values of the parameter $\mu$.