## 4 Results and Discussion
### The Variability of Index \(q\)
Therefore, in the last and most critical loading stage before failure, during which the coalescence of microcracks dominated the specimen, these processes were characterized by a low degree of organization and, according to NESM, the various subsystems that had formed were characterized by a low degree of mutual interaction, approximating a behavior similar to that of the Boltzmann-Gibbs statistics. In the case of the UCSS protocol (i.e., uniaxial compressive loading using stepped stress increments), the behavior of the entropic index \(q\) was studied during the six stress stages in which the stress increase was implemented at a constant rate. Each \(q\) value was assigned to the average normalized stress \(\overline{S}_{n}\) during its increasing stage (see Table 2). Subsequently, the behavior of index \(q\) was studied in the stress stages when the applied stress was kept constant. Especially during the last stress step under constant stress of 59.3 MPa, where the final fracture occurred, two values for the index \(q\) were calculated. The first value was calculated using the AE time intervals, during which the acoustic activity was attenuated (see Figure 3b), and the second was calculated when it showed a sharp increase before the fracture. The values of the entropic index \(q\), as well as the values of the parameter \(\beta_{q}\), are presented in Table 2. Figure 6 shows the evolution of the values of \(q\) as a  
Figure 5: The variability of the entropic index \(q\) and the variability of the acoustic activity, expressed in terms of the quantity \(F\) as functions of the normalized stress \(\overline{S}_{n}\). function of the normalized stress \(\overline{S}_{n}\) during the stages of the linear stress increase, and in the stages where the stress was kept constant. The result show that the entropic index \(q\) for the case of the UCSS loading protocol shows similar behavior to that of the entropic index \(q\) observed in the UC protocol. A maximum \(q\) value appears again just before the final fracture. The decrease observed in the values of \(q\) close to the final fracture (i.e., \(0.99\leq\overline{S}_{n}\leq 1.00\)) observed in UC is also confirmed here. Comparing the evolution of the \(q\) entropic indices of both loading protocols (UC and UCSS) in Figure 7, the following conclusions were drawn: A systematic increase in the \(q\) values is observed as the final fracture approaches, indicating that the mechanisms of creation, growth, and propagation of microcracks are characterized by an increasing degree of organization. The highest degree of organization dominated the fracture processes within the stress range \(0.96\leq\overline{S}_{n}\leq 0.99\) (see the yellow-shaded area in Figure 7). The UCSS protocol provides a better understanding concerning the rapid decrease in the values of \(q\) when the applied stress reached the specimen's strength limit. This, as mentioned above, can be attributed to the fact that the coalescence processes of the microcracks that lead to macrocrack failure are characterized by a low degree of organization, as well as the fact \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{5}{c}{**Increasing Stress**} & \multicolumn{5}{c}{**Constant Stress**} \\ \hline
**AE Hit Group** & \(\overline{S}_{n}\) & \(q\) & \(\beta_{q}\) (\(\mathbf{s}^{-1}\)) & **AE Hit Group** & \(\overline{S}_{n}\) & \(q\) & \(\beta_{q}\) (\(\mathbf{s}^{-1}\)) \\ \hline
1 & 0.868 & 1.19 & 9.41 & 1 & 0.881 & 1.14 & 3.65 \\
2 & 0.910 & 1.30 & 14.14 & 2 & 0.924 & 1.25 & 4.37 \\
3 & 0.940 & 1.37 & 23.50 & 3 & 0.948 & 1.34 & 5.60 \\
4 & 0.964 & 1.45 & 34.36 & 4 & 0.971 & 1.46 & 7.17 \\
5 & 0.982 & 1.50 & 57.50 & 5 & 0.986 & 1.52 & 10.04 \\
6 & 0.997 & 1.37 & 73.49 & 6a & 1.000 & 1.36 & 42.64 \\  & & & & & 6b & 1.000 & 1.22 & 47.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The entropic and mechanical parameters during the UCSS experiment for each consequent AE hit group.