Tsallis Distribution Decorated With Log-Periodic Oscillation

TL;DR

This paper explores how incorporating a complex nonextensivity parameter into the Tsallis distribution can explain log-periodic oscillations observed in various physical phenomena, suggesting a novel extension of the standard model.

Contribution

It introduces a new approach by allowing the nonextensivity parameter to be complex, providing a possible explanation for log-periodic oscillations in Tsallis distributions.

Findings

Log-periodic oscillations can be modeled by a complex nonextensivity parameter.

The approach suggests connections to complex heat capacity and complex probability.

This extension offers a new perspective on power-law behaviors in physics.

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.