Information, information gain, and efficiency of self-organizing systems close to instability points

Abstract

Selforganizing systems are those which can acquire macroscopic spatial, temporal, or spatio-temporal structures without interference from the outside by mere changes of control parameters. The slaving principle which has been derived for such systems close to their instability points allows one to give the probability distribution of the total system a specific form.

This in turn allows one to decompose information and information gain into a part which refers to the order parameters alone and a second part which is a sum over the information of the slaved modes averaged over the distribution of the order parameters. Close to instability points the information of the order parameters changes dramatically whereas the information of the slaved modes does not. Therefore close to these points it is sufficient to study the behavior of the order parameter information and information gain which is done explicitly for a large class of systems undergoing nonequilibrium phase transitions. It is shown how information and information gain as well as efficiency (in the sense defined in this paper) can be measured directly.