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The Fokker-Planck Equation (FPE) is a fundamental tool for the investigationof kinematic aspects of a wide range of systems. For systems governed by thenon-additive entropy $S_q$, the Plastino-Plastino Equation (PPE) is the correctgeneralization describing the kinematic evolution of such complex systems. Bothequations have been applied for investigations in many fields, and inparticular for the study of heavy quark evolution in the quark-gluon plasma. Inthe present work, we use this particular problem to compare the resultsobtained with the FPE and the PPE and discuss the different aspects of thedynamical evolution of the system according to the solutions for each equation.The comparison is done in two steps, first considering the modification thatresults from the use of a different partial derivative equation with the sametransport coefficients, and then investigating the modifications by using thenon-additive transport coefficients. We observe clear differences in thesolutions for all the cases studied here and discuss possible experimentalinvestigations that can indicate which of those equations better describes theheavy-quark kinematics in the medium. The results obtained here haveimplications in the study of anomalous diffusion in porous and granular media,in Cosmology and Astrophysics. The obtained results reinforce the validity ofthe relation $(q-1)^{-1}=(11/3)N_c-(4/3)(N_f/2)$, where $N_c$ and $N_f$ are,respectively, the number of colours and the effective number of flavours. Thisequation was recently established in the context of a fractal approach to QCDin the non-perturbative regime.

Comparative study of the heavy-quark dynamics with the Fokker-Planck Equation and the Plastino-Plastino Equation