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| In this talk I will discuss about some novel, recently published results [Antonopoulos et.al, 2014] that relate energy and information transfer with sensitivity to initial conditions in chaotic multi-dimensional Hamiltonian systems. I will show the relation among Kolmogorov-Sinai entropy, Lyapunov exponents, and upper bounds for the Mutual Information Rate calculated in the Hamiltonian phase space and on bi-dimensional subspaces. The main result is that the net amount of transfer from kinetic to potential energy per unit of time is a power-law of the upper bound for the Mutual Information Rate between kinetic and potential energies, and also a power-law of the Kolmogorov-Sinai entropy. Therefore, transfer of energy is related with both transfer and production of information. Finally, I will demonstrate the setup of an ``experimental'' implementation of a 1-dimensional communication channel based on a Hamiltonian system, and talk about the actual rate with which information is exchanged between the first and last particle of the channel. |
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