Dynamics of Non-stationary Processes That Follow the Maximum of Continuous Tsallis Entropy

In this paper a non-stationary processes that tend to maximize the Tsallis entropy are considered. Systems with discrete probability distribution for the Tsallis entropy have already been investigated on the basis of the Speed-Gradient principle. The evolution of probability density function and continuous form of the Tsallis entropy are considered. A set of equations describing dynamics of a system under the mass conservation and the energy conservation constraints is derived. The uniqueness of the limit distribution and asymptotic convergence of probability density function is examined for both constraints.