Chaotic diffusion: a Shannon entropy approach

PABLO CINCOTTA

Bristol

Seminario; Fluids and materials seminar; 2020

School of Mathematics Research, Univerity of Bristol

By means of theoretical arguments it is shown that the Shannonentropy is a quite sensitive approach to detect correlations in the state variables of a dynamical system.The formulation includes the analysis of the evolutionof a single variable of the system, for instance a given phase; thephase space variables of a 2-dimensional model or the actionspace of a 4-dimensional map or a 3dof Hamiltonian.The Shannon entropy provides a direct measure of the volume of thephase space occupied by a given trajectory as well as an accuratemeasure of the correlations among the successive values of the phasespace variables in any dynamical system, in particular when the motionis chaotic. Moreover, the time derivative of the entropy provides a goodestimate of the diffusion rate.