During the period of October 2011–January 2012, an increase of earthquake activity has been observed in the volcanic complex of Santorini Island, Greece. Herein, the magnitude distribution of earthquakes as well as the temporal distribution of seismicity are studied. The statistics of both parameters exhibit complexity that is evident in the frequency-magnitude distribution and the inter-event time distribution, respectively. Because of this, we have used the analysis framework of non-extensive statistical physics (NESP), which seems suitable for studying complex systems. The observed inter-event time distribution for the swarm-like earthquake events, as well as the energy and the inter-event earthquake energy distributions for the observed seismicity can be successfully described with NESP, indicating the inherent complexity of the Santorini volcanic seismicity along with the applicability of the NESP concept to volcanic earthquake activity, where complex correlations exist.

We analytically estimate the risk function of natural hazards (earthquakes, rockfalls, forestfires, landslides) by means of a non-extensive approach which is based on implementing the Tsallis entropy for the estimation of the probability density function (PDF) and introducing a phenomenological exponential expression for the damage function. The result leads to a power law expression as a special case and the b-value is given as a function of the non-extensive parameter q. A discussion of risk function dependence on the parameters of hazard PDF and damage function for various hazards is given.