Scalar curvature of systems with fractal distribution functions

2012/05/31 by Marcelo R. Ubriaco
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Boson #Complex Systems and Time Series Analysis #Curvature #Entropy (arrow of time) #Fractal #Fractal analysis #Fractal derivative #Fractal dimension #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Physics #Prescribed scalar curvature problem #Quantum mechanics #Scalar (mathematics) #Scalar curvature #Sectional curvature #Statistical Mechanics and Entropy #Statistical physics #cond-mat.stat-mech #math-ph #math.MP

paper · pdf · doi:10.1016/j.physleta.2012.07.023

9 pages, 2 figures, some typos were corrected, the Conclusions section was expanded

arxiv created 2012/07/21 · openalex publication_date 2012/07/31 · arxiv updated 2015/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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≠ 1 the scalar curvature is closer to zero implying that the fractal bosonic and fermionic systems are more stable than the standard ones.

Citations

• A simple mathematical model for anomalous diffusion via Fisher's information theory
• Ruppeiner geometry of anyon gas
• Thermodynamic geometry of fractional statistics
• A statistical mechanical approach to generalized statistics of quantum and classical gases