A measure of the criticality of a seismogenic system from the viewpoint of statistical physics

Despite the extreme complexity that characterizes the mechanism of the earthquake generation process, some phenomenological features seem to be identifiable in the collective properties of seismicity. It follows that the physics of many earthquakes has to be studied with a different approach than the physics of one earthquake and in this sense the use of statistical physics can be considered as necessary to understand the collective properties of earthquakes and to bridge the gap between physics-based models of individual events and statistics-based models of event populations. In this context the first question that arises is what type of statistical physics is appropriate to describe effects that affect different scales, variables with fractal distributions and long-range interactions. A possible answer could be non-extensive statistical physics (NESP), a generalization of the Boltzmann-Gibbs (BG) statistical physics that is based on the generalized entropic form, proposed by Tsallis in 1988, which recovers the BG entropy as a particular case. Following this approach, over the last two decades a series of studies has been performed on the power-law statistical distributions of energy release, inter-event time and spatial distances (Vallianatos et al., 2016). In this work we focus on the distribution of the magnitude and deal with some inferential aspects of the socalled q-exponential distribution in the Bayesian framework. The same distribution has been examined by Telesca (2012) according to the frequentist approach.