A LOCALLY OPTIMAL WAY TO APPROACH Q-GAUSSIAN DISTRIBUTION
q-Gaussian probability distribution is widely used in many fields of science nowadays including computer science, physics, biology and others. It is derived from the maximization of the Tsallis entropy under appropriate constraints. The maximum entropy states are already well investigated. But this can not be argued about the transient states which determine how the system moves to the final state. We propose a new equations describing dynamics of a complex nonstationary systems/processes which tend to the stationary q-Gaussian probability distribution under the proper set of constraints. We use the Speed-Gradient principle originated in the control theory, which is a locally optimal method to reach the given goal functional with the fastest possible way. Two types of constraints are examined: normal unbiased symmetric diffusion and its normalized form. The proposed equations allow to forecast the dynamics of complex non-equilibrium systems.