Four geographical zones are defined along the trench that is formed due to the subduction of the Nazca plate underneath the South American plate; they are denoted A, B, C and D from north to south; zones A, B and D had a major earthquake after 2010 (magnitude over 8.0), while zone C has not, thus offering a contrast for comparison. For each zone, a sequence of intervals between consecutive seisms with magnitudes greater than or equal to 3.0 is set up and then characterized by Shannon entropy and mutability. These methods show a correlation after a major earthquake in what is known as the aftershock regime but show independence otherwise. Exponential adjustments to these parameters reveal that mutability offers a wider range for the parameters to characterize the recovery compared to the values of the parameters defining the background activity for each zone before a large earthquake. It is found that the background activity is particularly high for zone A, still recovering for zone B, reaching values similar to those of zone A in the case of zone C (without recent major earthquake) and oscillating around moderate values for zone D. It is discussed how this can be an indication of more risk of an important future seism in the cases of zones A and C. The similarities and differences between Shannon entropy and mutability are discussed and explained.

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.

In this paper, we revisit the q-state clock model for small systems. We present results for the thermodynamics of the q-state clock model for values from $q=2$ to $q=20$ for small square lattices of $L\times L$ , with L ranging from $L=3$ to $L=64$ with free-boundary conditions. Energy, specific heat, entropy, and magnetization were measured. We found that the Berezinskii–Kosterlitz–Thouless (BKT)-like transition appears for $q>5$, regardless of lattice size, while this transition at $q=5$ is lost for $L<10$; for $q\le 4$, the BKT transition is never present. We present the phase diagram in terms of q that shows the transition from the ferromagnetic (FM) to the paramagnetic (PM) phases at the critical temperature $T_1$ for small systems, and the transition changes such that it is from the FM to the BKT phase for larger systems, while a second phase transition between the BKT and the PM phases occurs at $T_2$. We also show that the magnetic phases are well characterized by the two-dimensional (2D) distribution of the magnetization values. We made use of this opportunity to carry out an information theory analysis of the time series obtained from Monte Carlo simulations. In particular, we calculated the phenomenological mutability and diversity functions. Diversity characterizes the phase transitions, but the phases are less detectable as q increases. Free boundary conditions were used to better mimic the reality of small systems (far from any thermodynamic limit). The role of size is discussed.