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 relate...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2018 |
| País: | Argentina |
| Institución: | Universidad Nacional de La Plata |
| Repositorio: | SEDICI (UNLP) |
| Idioma: | inglés |
| OAI Identifier: | oai:sedici.unlp.edu.ar:10915/141472 |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/141472 |
| Access Level: | acceso abierto |
| Palabra clave: | Astronomía Física Chaotic diffusion Multidimensional dynamical systems Entropy Rate of diffusion |
| Sumario: | 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′, estimates the diffusion rate. We show that in the limiting case of near ergodicity, after an appropriate normalization, 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. |
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