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...

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Detalles Bibliográficos
Autores principales:	Giordano, Claudia Marcela, Cincotta, Pablo Miguel
Formato:	Articulo
Lenguaje:	Inglés
Publicado:	2018
Materias:	Astronomía Física Chaotic diffusion Multidimensional dynamical systems Entropy Rate of diffusion
Acceso en línea:	http://sedici.unlp.edu.ar/handle/10915/141472
Aporte de:	SEDICI (UNLP) de Universidad Nacional de La Plata

id	I19-R120-10915-141472
record_format	dspace
institution	Universidad Nacional de La Plata
institution_str	I-19
repository_str	R-120
collection	SEDICI (UNLP)
language	Inglés
topic	Astronomía Física Chaotic diffusion Multidimensional dynamical systems Entropy Rate of diffusion
spellingShingle	Astronomía Física Chaotic diffusion Multidimensional dynamical systems Entropy Rate of diffusion Giordano, Claudia Marcela Cincotta, Pablo Miguel The Shannon entropy as a measure of diffusion in multidimensional dynamical systems
topic_facet	Astronomía Física Chaotic diffusion Multidimensional dynamical systems Entropy Rate of diffusion
description	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.
format	Articulo Articulo
author	Giordano, Claudia Marcela Cincotta, Pablo Miguel
author_facet	Giordano, Claudia Marcela Cincotta, Pablo Miguel
author_sort	Giordano, Claudia Marcela
title	The Shannon entropy as a measure of diffusion in multidimensional dynamical systems
title_short	The Shannon entropy as a measure of diffusion in multidimensional dynamical systems
title_full	The Shannon entropy as a measure of diffusion in multidimensional dynamical systems
title_fullStr	The Shannon entropy as a measure of diffusion in multidimensional dynamical systems
title_full_unstemmed	The Shannon entropy as a measure of diffusion in multidimensional dynamical systems
title_sort	shannon entropy as a measure of diffusion in multidimensional dynamical systems
publishDate	2018
url	http://sedici.unlp.edu.ar/handle/10915/141472
work_keys_str_mv	AT giordanoclaudiamarcela theshannonentropyasameasureofdiffusioninmultidimensionaldynamicalsystems AT cincottapablomiguel theshannonentropyasameasureofdiffusioninmultidimensionaldynamicalsystems AT giordanoclaudiamarcela shannonentropyasameasureofdiffusioninmultidimensionaldynamicalsystems AT cincottapablomiguel shannonentropyasameasureofdiffusioninmultidimensionaldynamicalsystems
bdutipo_str	Repositorios
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The Shannon entropy as a measure of diffusion in multidimensional dynamical systems

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