Fractal structure and non extensive statistics

Abstract

The role played by non extensive thermodynamics in physical systems has been under intense debate for the last decades. With many applications in several areas, the Tsallis statistics has been discussed in details in many works and triggered an interesting discussion on the most deep meaning of entropy and its role in complex systems. Some possible mechanisms that could give rise to non extensive statistics have been formulated along the last several years, in particular a fractal structure in thermodynamics functions was recently proposed as a possible origin for non extensive statistics in physical systems. In the present work we investigate the properties of such fractal thermodynamical system and propose a diagrammatic method for calculations of relevant quantities related to such system. It is shown that a system with the fractal structure described here presents temperature fluctuation following an Euler Gamma Function, in accordance with previous works that evidenced the connections between those fluctuations and Tsallis statistics. Finally, the fractal scale invariance is discussed in terms of the Callan-Symanzik Equation.

22 pages, 3 figures

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• Dynamics in fractal spaces
• Bag-type Model with Fractal Structure
• Role of nuclear gluon distribution on particle production in heavy ion collisions
• Asymmetric Tsallis distributions for modelling financial market dynamics
• The evolution of Information entropy components in Relativistic Heavy-Ion Collisions
• Role of chemical potential at kinetic freeze-out using Tsallis non-extensive statistics in proton-proton collisions at the Large Hadron Collider
• The Tsallis entropy and the BKT-like phase transition in the impact parameter space for $pp$ and $\bar{p}p$ collisions
• Scale dependence of the q and T parameters of the Tsallis distribution in the process of jet fragmentation
• Fractal structure of hadrons and non-extensive statistics
• Non-extensive Effects on the QCD Equation of State and Fluctuations of Conserved Charges within Polyakov Quark Meson Model