A mathematical theory is proposed to describe the time evolution and fluctuations for the probability density and the entropy functions related to the state variable of nonlinear stochastic systems. The class of physical systems whose evolution can be modelled by nonlinear stochastic ordinary differential equations is considered and the evolution equation for the above specified functions is derived under suitable regularity conditions. Quantitative results in the applications are supplied on the basis of an analysis using the Adomian's decomposition method.