Introduction to Nonextensive Statistical Mechanics

Testing the Beta-Lognormal Model in Amazonian Rainfall Fields Using the Generalized Space q-Entropy

“…which, in the limit q → 1, recovers the usual Boltzmann-Gibbs-Shannon entropy, S [44], which is additive; in other words, for a system composed of any two (probabilistically) independent subsystems, the entropy S of the sum is the sum of their entropies [45], such that, if A and B are independent,…”

“…Therefore, our results suggest that the scaling exponent of S q across a range of scales in space and time reaches the same maximum value Ω sat = Ω ∼ 0.5, but the non-additive q value of saturation differs between space scaling (q ∼ 2.5) and time scaling (q ∼ 1.0). According to Tsallis [45], these results reflect the differences between the space and time dynamics of the system, although their connection with the physics of rainfall is an open problem. …”

“…Thus, the additivity depends on the functional form of the entropy in terms of probabilities [45]. Therefore, if A and B are independent, then…”

“…Taking the words of Tsallis [45], the value of q is useful to characterize the universal classes of nonadditivity. He argues that it is determined a priori by the microscopic dynamics of the system, which means that the thermostatistical entropy is not universal but depends on the system or, more precisely, on the non-additive universality class to which the system belongs.…”

“…He argues that it is determined a priori by the microscopic dynamics of the system, which means that the thermostatistical entropy is not universal but depends on the system or, more precisely, on the non-additive universality class to which the system belongs. It is worth mentioning the difference between additivity and extensivity, which is clearly explained in [45], as follows:…”