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Fractal Structure and Non-Extensive Statistics.
Airton Deppman1, Tobias Frederico2, Eugenio Megías3,4
1Instituto de Física, Universidade de São Paulo, Rua do Matão Travessa R Nr.187, Cidade Universitária, CEP 05508-090 São Paulo, Brazil.
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
This study explores fractal thermodynamics, linking fractal structures to non-extensive statistics and Tsallis statistics. Findings show temperature fluctuations follow an Euler Gamma Function, supporting connections to complex systems.
Area of Science:
- Thermodynamics
- Statistical Mechanics
- Complex Systems
Background:
- Non-extensive thermodynamics and Tsallis statistics are debated for complex systems.
- Fractal structures in thermodynamic functions are a proposed origin for non-extensive statistics.
Purpose of the Study:
- Investigate properties of fractal thermodynamical systems.
- Propose a diagrammatic method for calculating relevant quantities.
- Explore connections between fractal structures, temperature fluctuations, and Tsallis statistics.
Main Methods:
- Developed a diagrammatic calculation method for fractal thermodynamical systems.
- Analyzed temperature fluctuations within the fractal model.
- Utilized the Callan-Symanzik equation to discuss scale invariance.
Main Results:
- Demonstrated that fractal thermodynamical systems exhibit temperature fluctuations described by an Euler Gamma Function.
- Confirmed previous evidence linking temperature fluctuations to Tsallis statistics.
- Discussed the scale invariance properties of the fractal system.
Conclusions:
- Fractal structures provide a plausible mechanism for non-extensive statistics.
- The Euler Gamma Function accurately models temperature fluctuations in these systems.
- Further investigation into scale invariance using the Callan-Symanzik equation is warranted.
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