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 q 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.
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