Preprint Article Version 1 This version is not peer-reviewed

Fractal Structure and Non Extensive Statistics

Version 1 : Received: 27 June 2018 / Approved: 28 June 2018 / Online: 28 June 2018 (05:30:41 CEST)

A peer-reviewed article of this Preprint also exists.

Deppman, A.; Frederico, T.; Megías, E.; Menezes, D.P. Fractal Structure and Non-Extensive Statistics. Entropy 2018, 20, 633. Deppman, A.; Frederico, T.; Megías, E.; Menezes, D.P. Fractal Structure and Non-Extensive Statistics. Entropy 2018, 20, 633.

Journal reference: Entropy 2018, 20, 633
DOI: 10.3390/e20090633

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.

Subject Areas

fractal structure; non extensive statistics; Tsallis statistics; self-similarity; scale invariance

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