## 3 Data Analysis and Results
### The Mytilene Aftershock Sequence  
The 2017 Mytilene earthquake of \(M_{w}6.3\), took place at the coordinates (26.31, 38.85) (see more for location parameters in the Table 1) on 12 June at 12:28:37 GMT. This destructive offshore event occurred northeast of Chios and almost 15 km south of the southeast coast of Lesbos. In Virissa village, a collapsed building killed one person and injured 15 others due to a collapsed building and falling debris. Damage was reported in at least 12 villages across the southeast region of Lesvos, and there was additional impact along the Turkish coast [38]. Regarding the environmental impact of the earthquake, slope displacement and ground cracks occurred in many places in the disaster area. Also, tsunamis were reported in Pdomari Port [38]. A total of 1610 aftershocks were detected over the period between 12 June 2017 and 11 June 2018 (European Mediterranean Seismological Centre, EMSC). The aftershock area covers the region between the coordinates by longitudes 25.22\({}^{\circ}\) E-27.30\({}^{\circ}\) E and latitudes 38.23\({}^{\circ}\) N-39.22\({}^{\circ}\) N.  
In line with the analysis of the previous aftershock sequences, for the earthquake of Mytilene, we study the distribution of the interevent times. The value of \(q\) is equal to \(q\) = 1.68 (Figure 9a). The transition estimated to be at \(T_{c}\)\(\approx\) 10,761 s (Figure 9b). Since the most interevent times have \(T\) values \(T\)\(<\)\(T_{c}\), the parameter \(T_{c}\) (red dashed line in Figure 9c) confirms that the Tsallis entropy description dominates the early stages of the aftershocks' evolution. Figure 8: **(a)** The interevent times CDF of the 2017 \(M_{w}6.5\) Kos Earthquake, for the aftershocks with \(M\)\(>\)\(M_{c}\). The scarlet line is the \(Q\)-exponential fitting with \(q\) = 1.63. The change of colors indicates the crossover between the NESP (blue circles) and BG statistics (green triangles). **(b)** The \(ln_{Q}P(>\)\(T)\) as a function of \(T\), where the red line is the fitting with \(q\) = 1.63 and correlation coefficient 0.9935 up to \(T_{c}\). \(T_{c}\) value close to 15,005 s is suggested by the deviation from linearity. **(c)** Interevent time \(T\) evolution with time \(t\) since the main shock. The scarlet line illustrates the \(T_{c}\) value. In addition, and for all the aftershock sequences that were studied, we introduce a normalized parameter, \(x=T/T_{c}\), where \(x<1\) indicates the range where the Tsallis entropy describes the evolution of aftershocks sequence interevent times, while \(x>1\) is related to the Boltzmann-Gibbs (BG) process. This is because \(P(>T)=exp_{Q}(-T/T^{*})\) for \(T<T_{c}\). A deviation from the \(Q\)-exponential is present for all of the examined aftershock sequences when \(x>>1\) (i.e., \(T>>T_{c}\)). An inspection of Figure 10, where all aftershock sequences are plotted together, suggests that for \(0.01<x<1\), power-law scaling emerges for all the aftershock sequences, with a slope in the range 0.40-0.60, conforming to the \(q\) values calculated from the analysis (Table 1). The latter is expected since the asymptotic expression of Equation (6) is \(P(>T)\sim(T/T^{*})^{-\frac{1}{(Q-1)}}\) is a typical expression of a power law. Figure 10: The interevent times distribution \(P(>x)\) for all the studied aftershock sequences as a function of \(x=T/T_{c}\). Deviations from the \(Q\)-exponential operation are pronounced at \(T/T_{c}>>1\), for all sequences. Figure 9: (**a**) The interevent times CDF of the 2017 \(M_{\rm m}\)6.3 Mytilene Earthquake, for the aftershocks with \(M>M_{c}\). The scarlet line is the \(Q\)-exponential fitting with \(q=1.68\). The change of colors indicates the crossover between the NESP (blue circles) and physical BG statistics (green triangles). (**b**) The \(ln_{Q}P(>T)\) as a function of \(T\), where the red line is the fitting with \(q=1.68\) and correlation coefficient 0.9927 up to \(T_{c}\). \(T_{c}\) value close to 10,761 s is suggested by the deviation from linearity.