Nonlinear nonextensive kinetics and quantum mechanics

On the basis of generalized classical kinetic equations, reproducing the sta- tionary distribution of the Tsallis nonextensive thermostatistics, we postulate a nonlinear generalized Schroedinger equation. Such a dynamical equation satisfies the basic assumptions of the quantum mechanics under an appropriate generalization of the operator properties. In this framework, we apply the above introduced classical nonlinear equation to a phenomenological study of observable measured in the relativistic heavy-ion collisions experiments.