Production and transfer of energy and information in Hamiltonian systems

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 Ha...

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Bibliographic Details
Published in:PloS one 2014-02, Vol.9 (2), p.e89585-e89585
Main Authors: Antonopoulos, Chris G, Bianco-Martinez, Ezequiel, Baptista, Murilo S
Format: Article
Language:English
Subjects:
Chaos theory
Communications systems
Dynamical systems
Energy
Energy (Physics)
Energy Transfer
Entropy
Hamiltonian functions
Information systems
Information transfer
Initial conditions
Liapunov exponents
Mathematical analysis
Mathematical functions
Mathematics
Network topologies
Physics
Potential energy
Power law
Subspaces
Thermodynamics
Upper bounds
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Summary: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.
ISSN:1932-6203
1932-6203
DOI:10.1371/journal.pone.0089585