###### Abstract  
Acoustic emission (AE), recorded during uniaxial compressive loading with constantly increasing stress and stepped stress increments until the fracture of prismatic marble specimens, were analyzed in terms of non-extensive statistical mechanics (NESM). Initially introduced by [PERSON], NESM has proven to be an autonomous robust theoretical framework for studying fracture mechanisms and damage evolution processes during fracture experiments in specimens made of brittle materials. In the current work, the time intervals of the recorded AE data are analyzed in terms of NESM. For each examined specimen, the corresponding \(q\) entropic indices and the \(\beta_{q}\) parameters were calculated, and their variability in terms of the stress applied were studied. Furthermore, a possible linear relationship between the entropic index \(q\) and the parameter \(\beta_{q}\) was examined, and it was investigated whether the observed deviation from monotonicity between \(q\) and \(\beta_{q}\) may signal increased accumulation of damage, eventually leading to the final fracture of the specimens. Through this work, the emergence of an additional pre-failure indicator (i.e., the deviation from monotonicity between \(q\) and \(\beta_{q}\)) alongside well-established ones can provide further insight regarding the underlying crack development mechanisms and damage accumulation processes during the fracture of rock materials. acoustic emissions; non-extensive statistical mechanics; Tsallis entropy; uniaxial loading; pre-failure indicators +
Footnote †: journal: Applied Sciences  
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Footnote 1: institutetext: Department of Electrical and Electronics Engineering,some of parameters that are studied [5; 6; 7; 8; 9; 10; 11]. By utilizing the AE recordings during loading in rock materials, it has been observed that when the stress reaches a critical point, the acoustic activity increases dramatically [12; 13]. In addition, the amplitude-hit correlation can be used as one of the criteria for brittle or ductile failure [14]. Although different in scale, the phenomenon of acoustic emissions can be considered a process analogous to seismicity, as it has been found to exhibit similar statistics [15; 16]. Consequently, it can be reasonably assumed that seismicity analysis methodologies can be applied to the analysis of AEs after relevant modifications. Following this analogy, non-extensive statistical mechanics (NESM) are used herein to analyze the recorded acoustic data. NESM was firstly introduced by [PERSON] almost 30 years ago, and is a generalization of Boltzmann-Gibbs (BG) statistical mechanics [17; 18; 19] based on the concept of non-additive entropy. NESM has become a reliable theoretical framework for the study of complex systems in equilibrium and non-equilibrium states, systems exhibiting multifractality, self-similar structures, systems with long-range correlations, systems that show memory effects, etc. [20; 21]. Furthermore, NESM has been applied in several scientific fields (for applications, see Paragraph 1 of ref. [22] and the references cited therein). However, in the context of the present work, NESM applications have been used for the analysis of fracture processes at the laboratory scale in fracture experiments [23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33] and in field applications such as seismology [34; 35; 36; 37; 38]. In a previous work [32], the authors have examined the use of the entropic index \(q\) as a pre-failure indicator. Specifically, the AE timeseries was used for recording during mechanical loading until fracture when Greek Dionysos marble specimens were subjected to various loading schemes (i.e., diametral compression, three-point bending, direct tension), and cement mortar specimens subjected to three-point bending were analyzed under the concept of NESM. The results showed that the index \(q\) exhibited a systematic behavior, seemingly related to the different stages of the applied loading protocol and the consequent level of damage.