  Shannon information entropy is a natural measure of probability
(de)localization and thus (un)predictability in various procedures of data
analysis for model systems. We pay particular attention to links between the
Shannon entropy and the related Fisher information notion, which jointly
account for the shape and extension of continuous probability distributions.
Classical, dynamical and random systems in general give rise to time-dependent
probability densities and associated information measures. The induced dynamics
of Shannon and Fisher functionals reveals an interplay among various
characteristics of the considered diffusion-type systems: information,
uncertainty and localization while put against mean energy and its balance.
