Tsallis entropy on fractal sets

Abstract

In this article, we review fractal calculus ( $ F^{\alpha } $ -calculus) and define generalized Tsallis entropy on the fractal sets which is called fractal Tsallis entropy. We define q-fractal calculus to obtain q-Gaussian or generalized stable and Lévy distribution on fractal sets. The conditions for the nonlinear coupling of the statistical states are given. The relationship of fractal dimension which is defined in $ F^{\alpha } $ -calculus with q-parameter of the Tsallis entropy of the Hadron system is proposed.

Keywords

• fractal tsallis entropy
• fractal lévy distribution
• q-fractal calculus
• fractal q-gaussian
• thermo-fractal