Dimensional Regularization of Renyi's Statistical Mechanics

TL;DR

This paper investigates the mathematical singularities in Renyi's statistical mechanics, revealing physical implications such as gravitational effects through dimensional regularization of partition functions and mean energy.

Contribution

It introduces a novel analysis of poles in Renyi's statistical mechanics and applies dimensional regularization to explore their physical consequences.

Findings

Identification of poles in partition function and mean energy.

Discovery of gravitational effects linked to these poles.

Application of dimensional regularization to analyze singularities.

Abstract

We show that typical Renyi's statistical mechanics' quantifiers exhibit poles. We are referring to the partition function ${\cal Z}$ and the mean energy $<{\cal U}>$. Renyi's entropy is characterized by a real parameter $\alpha$. The poles emerge in a numerable set of rational numbers belonging to the $\alpha-$line. Physical effects of these poles are studied by appeal to dimensional regularization, as usual. Interesting effects are found, as for instance, gravitational ones.