AUTHOR=Treumann Rudolf A. , Baumjohann Wolfgang 

TITLE=Kinetic theory of information—the dynamics of information

JOURNAL=Frontiers in Physics

VOLUME=3

YEAR=2015

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2015.00019

DOI=10.3389/fphy.2015.00019

ISSN=2296-424X

ABSTRACT=<p>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 <inline-graphic xlink:href="fphy-03-00019-i0001.tif" xmlns:xlink="http://www.w3.org/1999/xlink" /><italic><sub>N</sub></italic> in a Hamiltonian system of large particle number <italic>N</italic> ≫ 1 is obtained. It is shown that the <italic>N</italic>-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 <inline-graphic xlink:href="fphy-03-00019-i0001.tif" xmlns:xlink="http://www.w3.org/1999/xlink" /><sub>1</sub> ≡ <inline-graphic xlink:href="fphy-03-00019-i0001.tif" xmlns:xlink="http://www.w3.org/1999/xlink" /> following the Bogoliubov prescription. The kinetic equation for <inline-graphic xlink:href="fphy-03-00019-i0001.tif" xmlns:xlink="http://www.w3.org/1999/xlink" /> 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.</p>