The Tsallis Parameter

TL;DR

This paper compares the exact stationary solution of a generalized Fokker-Planck equation with the maximum entropy solution derived from Tsallis entropy, revealing that agreement occurs only when the Tsallis parameter varies.

Contribution

It demonstrates the conditions under which the classical Tsallis distribution aligns with solutions of generalized Fokker-Planck equations, emphasizing the importance of a variable Tsallis parameter.

Findings

Exact solution matches MAXENT only with a non-constant Tsallis parameter

Highlights the limitations of assuming constant q in Tsallis statistics

Provides insights into the conditions for Tsallis distribution applicability

Abstract

The exact solution of a particular form of the stationary state generalized Fokker-Planck equations, which is given under certain conditions by the classical Tsallis distribution, is compared with the solution of the MAXENT equations obtained using the classical Tsallis entropy. The solutions only agree provided the Tsallis parameter, q, is no longer taken to be constant.