Thermodynamic criticality in seismicity: Uniqueness of surface-energy scaling in the fragment-asperity model

Abstract: We propose that a linear relation between the energy of stress-bearing interactions and the surface of contact within the fragment-asperity model for earthquakes. It reveals as the only one that leads to a closed elementary form for a well-defined total entropy as a function of non-extensivity parameter, $q$. By writing the total Tsallis entropy as a function of $q$, a critical range of values is identified: $1.4\lesssim q\lesssim 1.8$. Such interval of $q$-values corresponds to the strong variation of entropy and contains the most of reported results for this parameter determined for main-shocks around the world in recent decades, indicating the role of $q$ as a criticality indicator, more than just a fitting parameter.