Production and Transfer of Energy and Information in Hamiltonian Systems

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.

34 pages, 8 figures, accepted for publication in PLOS ONE

References in corpus (4)

• Work and information processing in a solvable model of Maxwell's demon
• Maxwell's Refrigerator: An Exactly Solvable Model
• Transmission of Information in Active Networks
• Stability of Simple Periodic Orbits and Chaos in a Fermi -- Pasta -- Ulam Lattice

Cited by in corpus (4)

• Do Brain Networks Evolve by Maximizing their Information Flow Capacity?
• Successful network inference from time-series data using Mutual Information Rate
• Inference of forex and stock-index financial networks based on the normalised mutual information rate
• Network inference combining mutual information rate and statistical tests