Abstract This study presents the results of Pressure Stimulated Currents (PSC) analysis using non-extensive statistical physics (NESP) approach when marble and amphibolite specimens were subjected to mechanical stress up to fracture. The specimens were subjected to a constant uniaxial stress, interrupted by an abrupt step-wise stress increase (Step-Stress Technique - SST) while concurrently the PSC emission was recorded. The loading protocol involved eight sequential steps of mechanical stress at a gradually higher level until the failure of the specimens. After each step, the stress was maintained constant until the PSC signal was restored to a final low value. After the PSC restoration the next stress step was applied. The recorded PSC temporal relaxation when the stress remained constant, was analyzed under the concept of NESP based on Tsallis’ entropy and the behavior of the entropic index q was studied for various stress levels. Throughout each next loading step at higher level, the entropic index q shows a progressive increase from 1.15 to 1.40 until the stress attains about 85% of the specimens’ total strength where it reaches a maximum value close to 1.4. When the applied stress becomes higher than the 85% of the specimens’ total strength, the entropic index q gradually decreases. It should be noted that this peak along with the subsequent decline of q coexists with the excessive damage development in the specimens’ bulk due to the applied mechanical stress. Taking into consideration the fact that the entropic index q quantifies the self-organization of the system, this behavior of q, for stress levels higher than 85% of the specimens’ ultimate stress strength, clearly corresponds to dynamic processes that dominate the system and guide the upcoming fracture. The above findings advocate the use of the entropic index q as a pre-failure indicator of the upcoming specimen fracture.