Dynamics of Information Entropies in Nonextensive Systems

TL;DR

This paper explores the time evolution of Tsallis entropy and generalized Fisher information in nonextensive Langevin systems with noise, providing analytical solutions and response analyses to external stimuli.

Contribution

It introduces analytical expressions for the dynamics of Tsallis entropy and Fisher information in nonextensive systems using a $q$-moment approach.

Findings

Analytical formulas for time-dependent Tsallis entropy and Fisher information.

Response behavior of information measures to pulse and sinusoidal inputs.

Application of the $q$-moment approach to nonextensive Langevin models.

Abstract

We have discussed dynamical properties of the Tsallis entropy and the generalized Fisher information in nonextensive systems described by the Langevin model subjected to additive and multiplicative noise. Analytical expressions for the time-dependent Tsallis entropy and generalized Fisher information have been obtained with the use of the $q$-moment approach to the Fokker-Planck equation developed in a previous study [H. Hasegawa, Phys. Rev. E {\bf 77}, 031133 (2008)]. Model calculations of the information entropies in response to an applied pulse and sinusoidal inputs have been presented.