Dynamics of non-stationary nonlinear processes that follow the maximum entropy principle (MaxEnt) for continuous probability distributions is considered. A set of equations describing the dynamics of probability density function (pdf) under the mass conservation and the energy conservation constraints is derived. The asymptotic convergence of evolving pdf and convergence of differential entropy are examined. It is shown that for pdfs with compact carrier the limit pdf is unique and coincides with the pdf obtained from Jaynes’s MaxEnt principle.