  Statistical properties of coupled dynamic-stochastic systems are studied
within a combination of the maximum information principle and the
superstatistical approach. The conditions at which the Shannon entropy
functional leads to a power-law statistics are investigated. It is demonstrated
that, from a quite general point of view, the power-law dependencies may appear
as a consequence of "global" constraints restricting both the dynamic phase
space and the stochastic fluctuations. As a result, at sufficiently long
observation times the dynamic counterpart is driven into a non-equilibrium
steady state whose deviation from the usual exponential statistics is given by
the distance from the conventional equilibrium.
