Frontiers in Physics (Mar 2015)
Kinetic theory of information -- the dynamics of information
Abstract
A kinetic approach to the notion of information is proposed, based on Liouville kinetic theory. The general kinetic equation for the evolution of the N-particle information $mathcal{I}_N$ in a Hamiltonian system of large particle number $Ngg 1$ is obtained. It is shown that the the $N$-particle information is strictly conserved. Defining reduced particle number information densities in phase space should be possible to obtain a kinetic equation for the ordinary one-particle information $mathcal{I}_1equiv mathcal{I}$ following the Bogoliubov prescription. The kinetic equation for $mathcal{I}$ is a kind of generalized Boltzmann equation with interaction term depending on the hierarchy of reduced informations. This term in its general form is the most general expression for the Kolmogorov entropy rate of evolution of the information.
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