Dynamic Tsallis entropy for simple model systems

TL;DR

This paper introduces the use of dynamic Tsallis entropy to analyze simple physical systems, demonstrating its ability to enhance signal features and extract information, especially in noisy environments.

Contribution

It applies dynamic Tsallis entropy to four model systems, revealing its effectiveness as a non-linear magnifier and its implications for non-Markovian behavior.

Findings

Small q values sharpen frequency spectra.

Tsallis entropy enhances information extraction in noisy systems.

Ideal gas remains non-Markovian regardless of q.

Abstract

In this paper we consider the dynamic Tsallis entropy and employ it for four model systems: (i) the motion of Brownian oscillator, (ii) the motion of Brownian oscillator with noise, (iii) the fluctuation of particle density in hydrodynamics limit as well as in (iv) ideal gas. We show that the small value of parameter nonextensivity $0<q<1$ works as non-linear magnifier for small values of the entropy. The frequency spectra become more sharp and it is possible to extract useful information in the case of noise. We show that the ideal gas remains non-Markovian for arbitrary values of $q$.