title: 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.
authors.affiliation: Department of Physics/ICSMB, University of Aberdeen, Aberdeen, United Kingdom.
authors.forename: Chris G
authors.initials: CG
authors.lastname: Antonopoulos
authors.affiliation: Department of Physics/ICSMB, University of Aberdeen, Aberdeen, United Kingdom.
authors.forename: Ezequiel
authors.initials: E
authors.lastname: Bianco-Martinez
authors.affiliation: Department of Physics/ICSMB, University of Aberdeen, Aberdeen, United Kingdom.
authors.forename: Murilo S
authors.initials: MS
authors.lastname: Baptista
mesh_terms: D004735:Energy Transfer; D013816:Thermodynamics