The maximum entropy states are intensively investigated nowadays because of numerous applications in a various fields of science. Nevertheless the dynamics of a system that tends to maximize its entropy is still not well investigated. We propose a new equations describing an evolution law for non-stationary processes that follow the maximum entropy production principle (MEPP). We use the Speed-Gradient principle originated in the control theory. We examine the uniqueness of the limit probability density function (pdf) and convergence of differential entropy. The proposed equations allow to forecast the dynamics of complex non-equilibrium systems.