Entropy of earthquakes: application to Vrancea earthquakes

Abstract

The entropy of earthquakes is derived by using the Gutenberg–Richter statistical distributions. Both canonical and microcanonical earthquake distributions are given, and Einstein’s fluctuation formula is deduced for earthquakes. The seismic activity of Vrancea in the period 1980–2019 is analyzed, for earthquakes with magnitude greater than two, and the results are compared with the theoretical results. It is shown that the parameter of the magnitude distribution exhibits a tendency of increasing with time, due to the accumulation of small-magnitude earthquakes, interrupted from time to time by ruptures towards smaller values, caused by earthquakes with greater magnitudes. These variations do not obey the normal distribution of the fluctuations. The (small) time variations of the distribution parameter provide a measure of the departure of the seismic activity from an equilibrium process. For Vrancea, these deviations are very small (up to 1% per year).