We found that the rare distribution of velocities in quasisteady states of the dipole-type Hamiltonian mean-field model can be explained by the Cairns-Tsallis distribution, which has been used to describe nonthermal electron populations of some plasmas. This distribution gives us two interesting parameters which allow an adequate interpretation of the output data obtained through molecular dynamics simulations, namely, the characteristic parameter $q$ of the so-called nonextensive systems and the $\alpha$ parameter, which can be seen as an indicator of the number of particles with nonequilibrium behavior in the distribution. Our analysis shows that fit parameters obtained for the dipole-type Hamiltonian mean-field simulated system are ad hoc with some nonthermality and nonextensivity constraints found by different authors for plasma systems described through the Cairns-Tsallis distribution.

We present a quantitative study of an online course developed during COVID19 sanitary emergency in Chile. We reconstruct the teaching–learning process considering the activity logs on digital platforms in order to answer the question of How do our students study? The results from the analysis evidence the complex adaptive character of the academic environment, which exhibits regularities similar to those found in financial markets (e.g., distributions of the daily time devoted to learning activities follow patterns like Pareto’s or Zipf’s law). Our empirical results illustrate (i) the relevance of economic notions in the understanding of the teaching–learning processes and (ii) the reliability of quantitative methods based on digital platforms to conduct experimental studies in this framework. We introduce in the present work a series of indicators to characterize the performance of professors, students’ follow-up of the course, and their learning progress by crossing information with the results of assessments. In this context, the learning rate appears as a key statistical descriptor for the allocation of the student workload.

Previously, we observed that the student workload follows an inverse relation with the learning rate (an application of the kinematic notion of speed contextualized to the learning process). Motivated by this finding, we propose a quantitative estimation of the learning rate using a different source of information: the historical records of final grades of a given course. According to empirical data analyzed in other similar studies, the distribution functions of final grades exhibit a regular pattern: a Gaussian behavior for the approval region and a homogeneous distribution for the failed one. This fact is combined with the incidence of student elimination–desertion rules for introducing two simple agent-based models. Our analysis is complemented by revisiting the performance indicators typically employed to characterize the student promotion and progression. We discuss some other performance indicators to characterize the learning advancement of students: the group learning rate and the learning curve. We compare the results of Monte Carlo simulations with empirical data, observing a good agreement in the behavior of performance indicators derived from these sources. This analysis suggests an adaptive method for the readjustment of the student workload (the number of academic credits) considering the group learning rates during a follow-up period, which resembles the readjustment of prices of goods (and services) in correspondence with the evolution of supply and demand.

This research studies information properties, such as complexity and disequilibrium, in the dipole-type Hamiltonian mean-field model. A fundamental analytical assessment is the partition function in the canonical ensemble to derive statistical, thermodynamical, and information measures. They are also analytical, dependent on the number of particles, consistent with the theory for high temperatures, and rising some limitations at shallow temperatures, giving us a notion of the classicality of the system defining an interval of temperatures where the model is well working.