  We present novel results that relate energy and information transfer with
sensitivity to initial conditions in chaotic multi-dimensional Hamiltonian
systems. We 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. Our 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. However, the power-law nature of this relation means
that a small increment of energy transferred leads to a relatively much larger
increase of the information exchanged. Then, we propose an ``experimental''
implementation of a 1-dimensional communication channel based on a Hamiltonian
system, and calculate the actual rate with which information is exchanged
between the first and last particle of the channel. Finally, a relation between
our results and important quantities of thermodynamics is presented.
