Solving the Poles of Nonextensive Statistical Physics

ZAMORA, DARÍO JAVIER

Trieste

Conferencia; 3rd EPS Conference on Statistical Physics of Complex Systems; 2021

EPS, European Physical Society

In order to statistically describe the dynamics of a plethora of complex systems, nonextensive statistics has been proposed. In the last decades, this new generalized statistical mechanical formalism have found a large variety of very successful applications, even beyond the realm of physics. It was found that classical Tsallis' theory exhibits poles in the partition function and the mean energy. This occurs at a countable set of the q line. I give a mathematical account of them. Further, by focusing attention upon the pole, one encounters interesting effects. The study and elimination of divergences of a physical theory is perhaps one of the most important aspects of theoretical physics nowadays. I propose two different approaches to solve those divergences: i a perturbative approximation, useful for the weak non-additive limit, and ii-dimensional regularization.