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Production and transfer of energy and information in Hamiltonian systems

Antonopoulos, CG and Bianco-Martinez, E and Baptista, MS (2014) 'Production and transfer of energy and information in Hamiltonian systems.' PLoS ONE, 9 (2). ISSN 1932-6203

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Abstract

We present novel results that relate energy and information transfer with sensitivity to initial conditions in chaotic multidimensional 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. © 2014 Antonopoulos et al.

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Jim Jamieson
Date Deposited: 20 Oct 2015 11:48
Last Modified: 17 Aug 2017 17:31
URI: http://repository.essex.ac.uk/id/eprint/15314

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