Information-theoretic approach to dynamics of stochastic systems

In the paper, we show how some basic informational quality measures (e.g. the Shannon entropy and the relative entropy/Kullback–Leibler divergence) defined for stochastic dynamical systems change in time and how they depend on the system properties and intensity of random disturbances. First, the Liouvillian systems (when randomness is present in the initial states only) are discussed and then various (linear and nonlinear) systems with random external excitations are treated in detail. Both, general and specific systems are considered, including numerical and graphical illustrations.