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Entropy Production in a Fractal System with Diffusive Dynamics
Rafael S Zola1, Ervin K Lenzi2, Luciano R da Silva3
1Departmento de Física, Universidade Tecnológica Federal do Paraná-Campus de Apucarana, Apucarana 86812-460, PR, Brazil.
Entropy (Basel, Switzerland)
|December 23, 2023
Summary
This study explores entropy production in fractal systems using nonlinear Fokker-Planck equations. Anomalous diffusion and subsystem impacts on total entropy were demonstrated, highlighting fractal dynamics.
Area of Science:
- Statistical Mechanics
- Complex Systems Theory
- Fractal Geometry
Background:
- Entropy production is a fundamental concept in thermodynamics and statistical mechanics.
- Fractal systems exhibit complex structures and dynamics not captured by Euclidean geometry.
- Nonlinear Fokker-Planck equations (NFEs) describe diffusion processes in various systems.
Purpose of the Study:
- To investigate entropy production in a fractal system with two subsystems under external forces.
- To analyze the impact of fractal geometry on diffusion dynamics and entropy.
- To explore analytical and numerical solutions for the system's behavior.
Main Methods:
- Application of the H-theorem to nonlinear Fokker-Planck equations.
- Formulation of a general NFE using Hausdorff derivatives to incorporate fractal metrics.
- Analytical and numerical investigation of system solutions.
Main Results:
- Demonstrated that each subsystem influences the total entropy production.
- Revealed anomalous diffusive processes due to the fractal nature of the system.
- Quantified the effect of fractal geometry on entropy and diffusion.
Conclusions:
- Fractal properties significantly alter diffusion dynamics and entropy production.
- The interplay between subsystems is crucial for understanding total system entropy.
- The developed NFE framework with Hausdorff derivatives is effective for fractal systems.
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