Kinetic theory of information -- the dynamics of information

TL;DR

This paper develops a kinetic theory framework for information dynamics in Hamiltonian systems, deriving a generalized Boltzmann-like equation for information evolution based on Liouville theory.

Contribution

It introduces a kinetic equation for information in large Hamiltonian systems, linking information conservation to a hierarchy of reduced information densities.

Findings

N-particle information is strictly conserved.

Derived a kinetic equation for one-particle information analogous to Boltzmann's equation.

Expressed the information evolution rate as a general Kolmogorov entropy rate.

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 $N\gg 1$ is obtained. It is shown that 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 $\mathcal{I}_1\equiv \mathcal{I}$ 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.