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Estimation of diffusion time with the Shannon entropy approach
Pablo M Cincotta1, Claudia M Giordano1
1Grupo de Caos en Sistemas Hamiltonianos, Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata and Instituto de Astrofísica de La Plata (CONICET), B1900FWA La Plata, B1900FWA, Argentina.
Physical Review. E
|July 19, 2023
Summary
This study refines the Shannon entropy method for estimating instability timescales in chaotic diffusion within Hamiltonian systems. The improved approach accurately predicts diffusion rates in the Arnold model, aligning well with numerical integration results.
Area of Science:
- * Physics
- * Celestial Mechanics
- * Dynamical Systems
Background:
- * Chaotic diffusion is a key phenomenon in multidimensional Hamiltonian systems.
- * Estimating instability timescales is crucial for understanding long-term system dynamics.
- * Previous applications of Shannon entropy proved effective for diffusion timescale estimation in specific systems.
Purpose of the Study:
- * To revisit and enhance the Shannon entropy approach for estimating instability timescales.
- * To apply the improved method to the Arnold model, focusing on local diffusion rates.
- * To validate the method by comparing its estimates with direct numerical integration.
Main Methods:
- * Application of the refined Shannon entropy approach.
- * Analysis of chaotic diffusion along the homoclinic tangle in the Arnold model.
- * Numerical integration of equations of motion for comparison.
Main Results:
- * The Shannon entropy method provides accurate local timescale estimates for Arnold diffusion-like processes.
- * The refined technique shows good agreement with diffusion times obtained from numerical integration.
- * The study focuses on regimes where resonance overlap is minimal.
Conclusions:
- * The enhanced Shannon entropy approach is a reliable tool for estimating diffusion timescales in Hamiltonian systems.
- * This method offers a valuable alternative to direct numerical integration for such estimations.
- * The findings contribute to a better understanding of chaotic dynamics in complex systems.
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