A feature indicative of non-equilibrium dynamic system is a fulfillment of a power law of distribution. We consider a number of simple models of generation of power-law distributions in seismic processes and in the processes of mineral deposits formation. As for seismicity, it is shown that deterministic earthquake prediction does not appear to be possible within the used model, whereas a probabilistic prognosis is feasible. Thus it seems possible to reconcile the well-known theoretical concept of unpredictability of earthquakes with the actual existence of algorithms realizing a non-trivial prognosis of strong earthquakes. As for processes of mineral deposits formation, models are discussed that permit to explain a generation of a power-law distribution of a number of large hydrocarbon and ore deposits from the stock values. A new interpretation is proposed of relatively less than could be expected from the extrapolation of a power distribution law number of deposits with relatively smaller stock values.
Power laws, dynamic systems, earthquake prognosis, deposit size distribution.
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