The Fokker-Planck Equation (FPE) is a fundamental tool for the investigation of kinematic aspects of a wide range of systems. The Plastino-Plastino Equation (PPE) is the correct generalization describing the kinematic evolution of complex systems consistent with q-statistics.

In the present work, we use this particular problem to compare the results obtained with the FPE and the PPE, and discuss the different aspects of the dynamical evolution of the system according to the solutions for each equation.

We observe clear differences in the solutions for all the cases studied here and discuss possible experimental investigations that can indicate which of those equations better describes the heavy-quark kinematics in the medium.

The results obtained here have implications in the study of anomalous diffusion in porous and granular media, in Cosmology and Astrophysics. The obtained results reinforce the validity of the relation (−1)−1=(11/3)−(4/3)(/2), where  and  are, respectively, the number of colours and the effective number of flavours. This equation was recently established in the context of a fractal approach to QCD in the non-perturbative regime.

E. Megías, A. Deppman, R. Pasechnik, C. Tsallis, Comparative study of the heavy-quark dynamics with the Fokker-Planck equation and the Plastino-Plastino equation, Physics Letters B 845 (2023) 138136.