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.
|Number of pages||13|
|Publication status||Published - 28 Feb 2014|
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Production and Transfer of Energy and Information in Hamiltonian Systems
Baptista, M. (Creator) & Antonopoulos, C. G. (Creator), Figshare, 13 Nov 2015
DOI: 10.1371/journal.pone.0089585, http://figshare.com/articles/_Production_and_Transfer_of_Energy_and_Information_in_Hamiltonian_Systems_/948182