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Entropy production and nonlinear Fokker-Planck equations
G A Casas1, F D Nobre, E M F Curado
1Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro, Brazil. gabrielaa@cbpf.br
This study analyzes entropy time rates in nonlinear systems using Fokker-Planck equations. It reveals how entropy production and flux relate to generalized entropic forms, applicable to complex systems.
Area of Science:
- Statistical Mechanics
- Nonlinear Dynamics
- Complex Systems
Background:
- Nonlinear Fokker-Planck equations model diverse physical phenomena.
- Generalized entropic forms extend classical thermodynamics.
- Understanding entropy dynamics is crucial for irreversible processes.
Purpose of the Study:
- Analyze the entropy time rate for systems governed by nonlinear Fokker-Planck equations.
- Investigate entropy production and flux in these systems.
- Relate findings to generalized entropic forms, including Tsallis and Kaniadakis entropies.
Main Methods:
- Analysis of entropy time rate using nonlinear Fokker-Planck equations.
- Study of entropy production and entropy flux.
- Examination of specific generalized entropic forms.
Main Results:
- The study provides a framework for analyzing entropy dynamics in nonlinear systems.
- It demonstrates how Boltzmann-Gibbs entropy emerges as a special case.
- The analysis is applicable to various generalized entropic forms.
Conclusions:
- Nonlinear Fokker-Planck equations offer a powerful tool for studying irreversible processes in complex systems.
- The framework developed is broadly applicable to systems described by generalized entropies.
- This research bridges statistical mechanics and nonlinear dynamics.
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