### Chaotic diffusion: a Shannon entropy approach

Fluids and Materials Seminar

7th May 2020, 2:00 pm – 3:00 pm

Fry Building, BlueJeans meeting

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

Related references:

Cincotta, P.M., Simó, C. 2020, Physica D, submitted

Cincotta, P.M., Shevchenko, I.I. 2020, Physica D, 402, 132235

Beaugé, C., Cincotta, P.M. 2019, Celestial Mechanics and Dynamical Astronomy, 131, 52

Cincotta, P.M., Giordano, C.M. 2018, Celestial Mechanics and Dynamical Astronomy, 130, 74

Giordano, C.M., Cincotta, P.M. 2018, Celestial Mechanics and Dynamical Astronomy, 130, 5

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