Non-additivity and Complex Systems

Many complex physical, chemical, economical, and biological systems manifest non-additivity characterized by long-tail distributions. Recently, we studied different time series that presented non-additive behavior in astrophysical sources, neuronal responses, dengue fever epidemics, proteins, sunspots, vehicle demand on the ferry-boat system, among others. That said, we studied light curves coming from astrophysical systems. We observe that astrophysical objects obey $q$-Gaussian distribution as probability density and the $q$-value increases for systems when the Tsallis entropy decreases. The classical concepts establish that the magnitude of spontaneous miniature end-plate potentials of mammals recorded at neuromuscular junctions is characterized by Gaussian statistics and that their intervals are randomly displayed, but it is not true. Power laws of protein mass, volume and solvent-accessible surface area are observed and $q$-Gaussian distributions fit well for this class of systems. When we analyzed the time series of vehicle demand on the ferry-boat system we note that stationary states of this dynamics process can be obtained by a nonlinear Fokker-Planck equation. On the other hand, the distribution of the sunspots obeys a $q$-exponential decay that suggests a non-extensive behavior. This observed characteristic seems to take an alternative interpretation of the sunspots dynamics. The present findings suggest us to propose a dynamic model of sunspots formation based on a nonlinear Fokker-Planck equation. The number of epidemiological dengue cases for each city follows a Self-Organized Criticality behavior (SOC). However, the analysis of the number of cases in Bahia exhibits a $q$-exponential distribution. To understand this different behavior, we analyzed the distribution of the power law of SOC ($\gamma $) for all biomes of Bahia. Finally, we show in this paper that nature often behaves as non-additive object and, sometimes, non-extensively.