Non-additive complex systems: Applications in Astrophysics, Chemistry and Engineering

In this work, a physical modeling for the stochastic dynamics based on nonlinear continuity equations is proposed. In this sense, self-similarity, long range correlations, self-organized criticality, among others, occurs in complex systems. Besides, non-Markovian stochastic processes might be noticed. The probability densities are solutions of the nonlinear Fokker-Planck equations that maximize the non-additive Tsallis entropy. Based on a nonlinear Fokker-Planck equation, a diffusion coefficient that it is proportional to the supercooled-liquid concentration is observed. The proposed model allows explaining the anomalous behavior of the diffusivity. We demonstrate that this new approach is consistent with experimental patterns. Besides, it could be applied to non-Arrhenius chemical kinetics. Then, a reaction-diffusion model to non-Arrhenius chemical kinetics is proposed. On the other hand, this non-Markovian model properly depicts the time evolution of a distribution of depth values of pits that were experimentally obtained. The solution of this equation in a steady-state regime is a $q$-Gaussian distribution, i.e. a long-tail probability distribution. In additional, the X-ray intensities of 142 light curves of cataclysmic variables, galaxies, pulsars, supernova remnants and other X-ray sources are studied. The X-ray light curves coming from astrophysical systems obey $q$-Gaussian distribution as probability density. This fact strongly suggests that these astrophysical systems behave in a nonextensive manner. Furthermore, the $q$ entropic indices for these systems were obtained and they provide an indication of the nonextensivity degree of each of these astrophysical systems. The $q$-value increases for systems if the Tsallis entropy decreases.