IFLP   13074
INSTITUTO DE FISICA LA PLATA
Unidad Ejecutora - UE
congresos y reuniones científicas
Título:
On the divergences of nonextensive statistics and how to solve them
Autor/es:
ZAMORA, DARÍO JAVIER
Reunión:
Conferencia; CCS2020 - Conference on Complex System 2020; 2020
Institución organizadora:
Complex Systems Society
Resumen:
After more than 140 years of impressive success there is no doubt that the Boltzmann-Gibbs(BG) entropy is the correct one to be used for a wide and important class of physical systems,basically those are mixing and ergodic. However, a plethora of physical complex systems existsfor which such simplifying dynamical hypotheses are violated. Corresponding anomalies arefound in a variety of quantum systems as well. In order to statistically describe the dynamics ofsuch systems, various generalized forms of statistical mechanics have been proposed such asthose using the non-additive entropies [1], kappa distributions, superstatistical approaches,among various others. In the last decades, these new generalized statistical mechanicalformalisms have found a large variety of very successful applications in complex systems, evenbeyond the realm of physics.It was found in [2] that classical Tsallis´ theory exhibits poles in the partition function and themean energy. This occurs at a countable set of the q-line (see, for example, figure 1). I give amathematical account of them. Further, by focusing attention upon the pole, one encountersinteresting effects.Divergences are an important topic in theoretical physics. Indeed, the study and elimination ofdivergences of a physical theory is perhaps one of the most important aspects of theoreticalphysics.I propose two different approaches to solve those divergences: i- a perturbative approximation[3], useful for the weak non-additive limit, and ii- dimensional regularization [4].