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arXiv · 1310.1223

Production and Transfer of Energy and Information in Hamiltonian Systems

Ch. G. Antonopoulos·E. Bianco-Martinez·M. S. Baptista
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Abstract

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.

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Ch. G. Antonopoulos, E. Bianco-Martinez, M. S. Baptista. 2014-01-23. Production and Transfer of Energy and Information in Hamiltonian Systems. https://doi.org/10.1371/journal.pone.0089585

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