The problem of stochastic stability of discrete dynamic systems is examined from the point of view of entropy. Entropy, as it was defined by Shannon, is a measure of average uncertainty of the system state. Conditions are found which guarantee reduction of the entropy. Several classes of systems are considered : linear with constant or time-varying coefficients and non-linear systems. The necessary and sufficient conditions are rather weak because of the generality of entropy, but simple in nature. The sufficient conditions are strong but more severe.