Information, Information Gain, and Efficiency of Self-Organizing Systems Close to Their Instability Points

Abstract

In this section we wish to further elaborate on the results of the preceding chapter. There we have shown that we may split the joint probability distribution function P(ξ _u , ξ _s ) which refers to the order parameters, ξ _u , and enslaved-mode amplitudes, ξ _s , into a product of the form

$$P\left( {{\xi _u},{\xi _s}} \right)\prod\limits_s {{P_s}\left( {{\xi _s}\left| {{\xi _u}} \right.} \right)f\left( {{\xi _u}} \right)}$$

((7.1))

.