The thermostatistical formalism derived from the \(S_q\) nonadditive entropies is nowadays widely applied to the study of complex phenomena in physics, biology, and other areas. The q-MaxEnt, power-law probability densities, that optimize the \(S_q\) entropies, play a central role within this formalism. Previous research indicates that the q-MaxEnt densities may arise naturally from the behavior of computational neural networks for associative memory, that are key ingredients for developing mathematical models for diverse mental phenomena, including neurosis, creativity, and the interplay between consciousness and unconsciousness. Power-law densities, akin to the q-MaxEnt ones, have also been experimentally observed in brain dynamics. We analyze here, from the point of view of the \(S_q\) -thermostatistics, features of the information flow in a nonlinear Fokker-Planck formulation of the continuous-time evolution of interacting neurons in Hopfield-like models. The present study provides a new perspective on the possible dynamical mechanisms giving rise to power-law-like behavior in neural network dynamics. In particular, our present developments shed new light on the process through which time-dependent solutions of the network’s Fokker-Planck equation evolve towards q-MaxEnt, stationary densities.