Analysis of Two Large Earthquakes in the South Pacific Coast of Mexico Using Rényi Entropy

We present a study on the behavior of Rényi entropy for earthquake magnitudes, focusing on two large-magnitude events in the Pacific coast of Mexico: the M8.2 Tehuantepec earthquake in 2017 and the M7.7 Michoacán earthquake in 2022. Based on the discrete version of Rényi entropy, we show that entropy decreases before the mainshocks occur and subsequently exhibits an abrupt increase before returning to stable values. The behavior of Rényi entropy in terms of the control parameter α, which either rewards or penalizes regions of the distribution, exhibits differences in the rate at which entropy decreases as α increases before, during, and after an earthquake. This abrupt change in entropy exhibits characteristics analogous to those observed in critical transitions.