Production and transfer of energy and information in Hamiltonian systems

Chris G Antonopoulos, Ezequiel Bianco-Martinez, Murilo S Baptista

Research output: Contribution to journalArticle

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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.
Original languageEnglish
Article numbere89585
Number of pages13
JournalPloS ONE
Volume9
Issue number2
DOIs
Publication statusPublished - 28 Feb 2014

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Hamiltonians
Energy Transfer
information systems
Entropy
energy transfer
Potential energy
Thermodynamics
entropy
energy
Kinetic energy
kinetics
information exchange
Kinetics
thermodynamics

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Production and transfer of energy and information in Hamiltonian systems. / Antonopoulos, Chris G; Bianco-Martinez, Ezequiel; Baptista, Murilo S.

In: PloS ONE, Vol. 9, No. 2, e89585, 28.02.2014.

Research output: Contribution to journalArticle

Antonopoulos, Chris G ; Bianco-Martinez, Ezequiel ; Baptista, Murilo S. / Production and transfer of energy and information in Hamiltonian systems. In: PloS ONE. 2014 ; Vol. 9, No. 2.
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