Experimental evidence of a non-extensive statistical physics behaviour of fracture in triaxially deformed Etna basalt using acoustic emissions

Using acoustic emission (AE) data, we apply the concepts of non-extensive statistical physics (NESP) to the time intervals and Euclidean distances between two consecutive AE. The application of NESM is appropriate to systems such as fracture where non-linearity, long-range interactions and scaling are important. We find that the AE scalar moment distribution and the inter-event time distribution reflect a sub-additive system with thermodynamic q -values of qM =1.82 and qτ =1.34, respectively, while the inter-event distance distribution follows a q -statistics, with qD =0.65, supporting the conclusion of the so-called "non-extensive spatio-temporal duality". The results regarding the inter-event time distribution are discussed using the complementary to the NESP approach of superstatistics which is based on a superposition of ordinary local equilibrium statistical mechanics, using a suitable intensive parameter β that fluctuates on a relatively large temporal scale. This analysis leads us to conclude that a low number of degrees of freedom describe the process which generates the distribution of AE.