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Is plate tectonics a case of non-extensive thermodynamics?

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  • Vallianatos, Filippos
  • Sammonds, Peter

Abstract

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.

Suggested Citation

  • Vallianatos, Filippos & Sammonds, Peter, 2010. "Is plate tectonics a case of non-extensive thermodynamics?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4989-4993.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:21:p:4989-4993
    DOI: 10.1016/j.physa.2010.06.056
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    Citations

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    Cited by:

    1. Ferreira, Douglas S.R. & Ribeiro, Jennifer & Oliveira, Paulo S.L. & Pimenta, André R. & Freitas, Renato P. & Papa, Andrés R.R., 2020. "Long-range correlation studies in deep earthquakes global series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).
    2. Pavlos, G.P. & Karakatsanis, L.P. & Xenakis, M.N. & Pavlos, E.G. & Iliopoulos, A.C. & Sarafopoulos, D.V., 2014. "Universality of non-extensive Tsallis statistics and time series analysis: Theory and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 58-95.
    3. Vallianatos, Filippos, 2018. "A non extensive view of electrical resistivity spatial distribution estimated using inverted Transient Electromagnetic responses in a karstified formation (Keritis basin, Crete, Greece)," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 171-178.
    4. Scherrer, T.M. & França, G.S. & Silva, R. & de Freitas, D.B. & Vilar, C.S., 2015. "Nonextensivity at the Circum-Pacific subduction zones—Preliminary studies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 426(C), pages 63-71.
    5. Cartwright-Taylor, Alexis & Vallianatos, Filippos & Sammonds, Peter, 2014. "Superstatistical view of stress-induced electric current fluctuations in rocks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 414(C), pages 368-377.
    6. Vallianatos, Filippos & Koutalonis, Ioannis & Chatzopoulos, Georgios, 2019. "Evidence of Tsallis entropy signature on medicane induced ambient seismic signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 35-43.
    7. Papadakis, Giorgos & Vallianatos, Filippos & Sammonds, Peter, 2016. "Non-extensive statistical physics applied to heat flow and the earthquake frequency–magnitude distribution in Greece," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 135-144.

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