The Shannon entropy as a measure of diffusion in multidimensional dynamical systems

The Shannon entropy as a measure of diffusion in multidimensional dynamical systems In the present work, we introduce two new estimators of chaotic diffusion based on the Shannon entropy. Using theoretical, heuristic and numerical arguments, we show that the entropy, S, provides a measure of the diffusion extent of a given small initial ensemble of orbits, while an indicator related with the time derivative of the entropy, $$S'$$ S ′ , estimates the diffusion rate. We show that in the limiting case of near ergodicity, after an appropriate normalization, $$S'$$ S ′ coincides with the standard homogeneous diffusion coefficient. The very first application of this formulation to a 4D symplectic map and to the Arnold Hamiltonian reveals very successful and encouraging results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Celestial Mechanics and Dynamical Astronomy Springer Journals

The Shannon entropy as a measure of diffusion in multidimensional dynamical systems

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Publisher
Springer Netherlands
Copyright
Copyright © 2018 by Springer Science+Business Media B.V., part of Springer Nature
Subject
Physics; Astrophysics and Astroparticles; Dynamical Systems and Ergodic Theory; Aerospace Technology and Astronautics; Geophysics/Geodesy; Classical Mechanics
ISSN
0923-2958
eISSN
1572-9478
D.O.I.
10.1007/s10569-018-9832-x
Publisher site
See Article on Publisher Site

Abstract

In the present work, we introduce two new estimators of chaotic diffusion based on the Shannon entropy. Using theoretical, heuristic and numerical arguments, we show that the entropy, S, provides a measure of the diffusion extent of a given small initial ensemble of orbits, while an indicator related with the time derivative of the entropy, $$S'$$ S ′ , estimates the diffusion rate. We show that in the limiting case of near ergodicity, after an appropriate normalization, $$S'$$ S ′ coincides with the standard homogeneous diffusion coefficient. The very first application of this formulation to a 4D symplectic map and to the Arnold Hamiltonian reveals very successful and encouraging results.

Journal

Celestial Mechanics and Dynamical AstronomySpringer Journals

Published: Apr 28, 2018

References

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