Multifractal spectrum of the phase space related to generalized thermostatistics

TL;DR

This paper models the multifractal spectrum of phase space in generalized thermostatistics using hyperbolic tangent deformations of statistical weight exponents, revealing how monofractal counts vary with phase space volume.

Contribution

It introduces a novel modeling approach for the multifractal spectrum using deformed hyperbolic tangent functions linked to Tsallis and Kaniadakis exponentials.

Findings

The spectrum function $f(d)$ increases monotonically from -1 to 1 as $d$ goes from 0 to 1.

The number of monofractals increases with phase space volume at small dimensions.

The number of monofractals decreases as the dimension approaches 1.

Abstract

We consider the set of monofractals within a multifractal related to the phase space being the support of a generalized thermostatistics. The statistical weight exponent $\tau(q)$ is shown to can be modeled by the hyperbolic tangent deformed in accordance with both Tsallis and Kaniadakis exponentials whose using allows one to describe explicitly arbitrary multifractal phase space. The spectrum function $f(d)$, determining the specific number of monofractals with reduced dimension $d$, is proved to increases monotonically from minimum value $f=-1$ at $d=0$ to maximum $f=1$ at $d=1$. The number of monofractals is shown to increase with growth of the phase space volume at small dimensions $d$ and falls down in the limit $d\to 1$.