Scalar curvature of systems with fractal distribution functions

TL;DR

This paper investigates the scalar curvature of systems with fractal distribution functions, revealing that for non-standard moment parameters, these systems exhibit increased stability compared to classical, bosonic, and fermionic systems.

Contribution

It introduces a method to compute the scalar curvature for systems with fractal distribution functions and analyzes stability implications for different quantum statistics.

Findings

Scalar curvature approaches zero for q ≠ 1, indicating increased stability.

Fractal systems show different geometric properties compared to standard systems.

Stability is enhanced in fractal bosonic and fermionic systems.

Abstract

Starting with the relative entropy for two close statistical states we define the metric and calculate the scalar curvature $R$ for systems with classical, boson and fermion fractal distribution functions with moment order parameter $q$. In particular, we find that for $q\neq 1$ the scalar curvature is closer to zero implying that the fractal bosonic and fermionic systems are more stable than the standard ones.