Tsallis Distribution Decorated With Log-Periodic Oscillation

Abstract

In many situations, in all branches of physics, one encounters power-like behavior of some variables which are best described by a Tsallis distribution characterized by a nonextensivity parameter $q$ and scale parameter $T$. However, there exist experimental results which can be described only by a Tsallis distributions which are additionally decorated by some log-periodic oscillating factor. We argue that such a factor can originate from allowing for a complex nonextensivity parameter $q$. The possible information conveyed by such an approach (like the occurrence of complex heat capacity, the notion of complex probability or complex multiplicative noise) will also be discussed.

Comments: 17 pages, 1 figure. The content of this article was presented by Z. Wlodarczyk at the SigmaPhi2014 conference at Rhodes, Greece, 7-11 July 2014. To be published in Entropy (2015)