The mechanical description of the seismic cycle has an energetic analogy in terms of statistical physics and the second law of thermodynamics. In this context, an earthquake can be considered a phase transition, where continuous reorganization of stresses and forces reflects an evolution from equilibrium to non-equilibrium states, and we can use this analogy to characterize the earthquake hazard of a region. In this study, we used 8 years (2007–2014) of high-quality Integrated Plate Boundary Observatory Chile (IPOC) seismic data for > 100 000 earthquakes in northern Chile to test the theory that Shannon entropy, H, is an indicator of the equilibrium state of a seismically active region. We confirmed increasing H reflects the irreversible transition of a system and is linked to the occurrence of large earthquakes. Using variation in H, we could detect major earthquakes and their foreshocks and aftershocks, including the 2007 M_w 7.8 Tocopilla earthquake, the 2014 M_w 8.1 Iquique earthquake, and the 2010 and 2011 Calama earthquakes (M_w 6.6 and 6.8, respectively). Moreover, we identified possible periodic seismic behaviour between 80 and 160 km depth.

Seismic data have improved in quality and quantity over the past few decades, enabling better statistical analysis. Statistical physics has proposed new ways to deal with these data to focus the attention on specific matters. The present paper combines these two progressions to find indicators that can help in the definition of areas where seismic risk is developing. Our data comes from the IPOC catalog for 2007 to 2014. It covers the intense seismic activity near Iquique in Northern Chile during March/April 2014. Centered in these hypocenters we concentrate on the rectangle $La{t}_{-22}^{-18}$ and $Lo{n}_{-68}^{-72}$ and deepness between 5 and 70 km, where the major earthquakes originate. The analysis was performed using two complementary techniques: Tsallis entropy and mutability (dynamical entropy). Two possible forecasting indicators emerge: (1) Tsallis entropy (mutability) increases (decreases) broadly about two years before the main $M_{W}8.1$ earthquake. (2) Tsallis entropy (mutability) sharply decreases (increases) a few weeks before the $M_{W}8.1$ earthquake. The first one is about energy accumulation, and the second one is because of energy relaxation in the parallelepiped of interest. We discuss the implications of these behaviors and project them for possible future studies.

We propose the use of entropy, H, as an indicator of the equilibrium state of a seismically active region (seismic system). The relationship between an increase in H and the occurrence of a great earthquake in a study area can be predicted by acknowledging the irreversible transition of a system. From this point of view, the seismic system evolves from an unstable initial state (due to external stresses) to another, where the stresses have dropped after the earthquake occurred. It is an irreversible transition that entails an increase in entropy. Five seismic episodes were analyzed in the south of the Iberian Peninsula, the Alboran Sea (Mediterranean Sea), and the North of Morocco: two of them of moderate-high magnitude (Al Hoceima, 2004 and 2016) and three of them of moderate-low magnitude (Adra, 1993–1994; Moron, 2007; and Torreperogil, 2012–2013). The results are remarkably in line with the theoretical forecasts; in other words: an earthquake, understood as an irreversible transition, must suppose an increase in entropy.

We have conducted an entropy analysis in Alaska, a seismic-rich region in a subduction zone that exhibits a nontrivial behavior: the subduction arc alters the seismic activity from the eastern zone to the western zone, demonstrating a decrease in activity along the subduction. We analyze this zone through the Tsallis entropy and the mutability (or dynamic entropy) for the first time. Considering 13 870 seismic events after appropriate filtering, we analyzed a data set for the selected Alaska zone between 2000 and 2023. We have found agreement between the results for the two entropies. We have followed the value of the q parameter of the Tsallis entropy (S_q) finding values between 1.70 and 1.85, in concordance with values found in other seismic regions of the planet. The values of S_q decrease slightly over time but show a broad increase before the major earthquakes. Just opposite to Tsallis entropy, mutability shows a tendency to decrease prior to the major earthquakes. We used the simpler mutability method to further analyze this zone upon dividing the region into four subzones. The results show how mutability can identify the seismic activity in each zone. This study shows how an entropy approach can shed light on understanding the seismicity in subduction zones.