  The theoretical basis of neuronal coding, associated with short term
degradation in synaptic transmission, is a matter of debate in the literature.
In fact, electrophysiological signals are commonly characterized as inversely
proportional to stimulus intensity. Among theoretical descriptions of this
phenomenon, models based on $1/f$-dependency are employed to investigate the
biophysical properties of the short term synaptic depression. In this work we
formulated a model based on a paradigmatic \textit{q}-differential equation to
obtain a generalized formalism useful for investigation of nonextensivity in
this specific type of synaptic plasticity. Our analysis reveals nonextensivity
in data from electrophysiological recordings and also a statistical crossover
in neurotransmission. In particular, statistical transitions providesadditional
support to the hypothesis of heterogeneous release probability of
neurotransmitters. On the other hand, the simple vesicle model agrees with data
only at low frequency stimulations. Thus, the present work presents a method to
demonstrate that short-term depression is not only governed by random
mechanisms but also by a nonextensive behavior. Our findings also conciliate
morphological and electrophysiological investigations into a coherent
biophysical scenario.
