Curl forces and the nonlinear Fokker-Planck equation
R S Wedemann1, A R Plastino2, C Tsallis3,4
1Instituto de Matemática e Estatística, Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, 20550-900 Rio de Janeiro, Rio de Janeiro, Brazil.
Physical Review. E
|January 14, 2017
Summary
Nonlinear Fokker-Planck equations with curl drift forces can have stationary solutions. These solutions satisfy an H theorem using S_{q} entropy, relevant for complex systems.
Area of Science:
- Statistical Mechanics
- Nonlinear Dynamics
- Complex Systems
Background:
- Nonlinear Fokker-Planck equations model complex systems.
- Curl drift forces introduce unique dynamics.
- Understanding stationary states is crucial for system stability.
Purpose of the Study:
- Investigate nonlinear Fokker-Planck equations with curl drift.
- Determine conditions for stationary solutions.
- Analyze the thermodynamic properties of these solutions.
Main Methods:
- Mathematical analysis of evolution equations.
- Derivation of conditions for stationary q-exponential solutions.
- Application of H theorem using S_{q} entropy.
Main Results:
- Conditions for stationary q-exponential solutions identified.
- Stationary solutions lead to an H theorem.
- Analytical time-dependent q-Gaussian solutions derived for a specific model.
Conclusions:
- The study provides insights into the behavior of nonlinear Fokker-Planck equations with curl drift.
- The findings are relevant to systems exhibiting overdamped motion and short-range interactions.
- Potential applications exist in physics, astronomy, and biology, including type-II superconductors.
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