Complexity and disequilibrium in the dipole-type Hamiltonian mean-field model.

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.

Statistical dynamics of driven systems of confined interacting particles in the overdamped-motion regime.

Systems consisting of confined, interacting particles doing overdamped motion admit an effective description in terms of nonlinear Fokker-Planck equations. The behavior of these systems is closely related to the power-law entropies and can be interpreted in terms of the -based thermostatistics. The connection between overdamped systems and the measures provides valuable insights on diverse physical problems, such as the dynamics of interacting vortices in type-II superconductors.

Derivation and analytical solutions of a non-linear diffusion equation applied to non-constant heat conductivity and ionic diffusion in glasses.

This paper derives a non-linear diffusion equation discussing two possible applications: the ionic diffusion in glasses and temperature-dependent conductivity in semiconductors. The first equation is a logarithmic diffusion derived formally from the continuity of ion concentration, but the latter is a more phenomenological example. A power-law ansatz with time-dependent parameters maximizes a non-standard entropy and gives a set of coupled motion equations we can solve analytically.

Analyzing the 2019 Chilean social outbreak: Modelling Latin American economies.

In this work, we propose a quantitative model for the 2019 Chilean protests. We utilize public data for the consumer price index, the gross domestic product, and the employee and per capita income distributions as inputs for a nonlinear diffusion-reaction equation, the solutions to which provide an in-depth analysis of the population dynamics. Specifically, the per capita income distribution stands out as a solution to the extended Fisher-Kolmogorov equation.