Scalar curvature of systems with fractal distribution functions

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

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

References in corpus (5)

• Exact solution for mean first-passage time on a pseudofractal scale-free web
• Thermodynamic Geometry of Deformed Bosons and Fermions
• Thermodynamic Geometry of Fractional Statistics
• Ruppeiner Geometry of Anyon Gas
• Nonperturbative Thermodynamic Geometry of Anyon Gas

Cited by in corpus (6)

• Thermodynamics of bosons systems related to Dunkl differential-difference operators
• Stability and anyonic behavior of systems with M-statistics
• Generalized Nonlinear Proca Equation and its Free-Particle Solutions
• Geometry of Quantum Group invariant systems
• Intrinsic Attractive and Repulsive Interactions: From Classical to Quantum Gases in the Generalized Maxwell-Boltzmann Distribution
• Density matrix for a consistent non-extensive thermodynamics