Is plate tectonics a case of non-extensive thermodynamics?

Bird (2003) [5] proposed that the distribution of areas of the tectonic plates follows a power law and that this distribution fitted well with the concepts of a few major plates and a hierarchical self-similar organization of blocks at the boundary scale, a fractal plate distribution and a self-organized system. Here we apply the concepts of non-extensive statistical mechanics (NESM) to plate tectonics. The application of NESM is appropriate to systems such as tectonic plates where non-linearity, long-range interactions, memory effects and scaling are important. We calculate the probability density function for the areas of the tectonic plates. Our results show that three classes (small, intermediate and large) of tectonic plates can be distinguished, which is consistent with the observations of Bird. Furthermore, taking into account that for the intermediate class of tectonic plates the cumulative frequency distribution behaves as a power law with exponent 1/3, we estimate a thermodynamic q parameter of q=1.75, which supports the conclusion that the plate tectonics system is a sub-extensive one.