2018/05/28 by Ignacio S. Gomez, Gomez, Ignacio S., Ernesto P. Borges +3
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Fractional Differential Equations Solutions #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.1805.11157
openalex publication_date 2018/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work we consider the Fisher metric which results from the Hessian of the relative entropy group, that we called Fisher metric group, and we obtain the corresponding ones to the Boltzmann-Gibbs, Tsallis, Kaniadakis and Abe-Borges-Roditi classes. We prove that the scalar curvature of the Fisher metric group results a multiple of the standard Fisher one, with the factor of proportionality given by the local properties of the entropy group. For the Tsallis class, the softening and strengthening of the scalar curvature is illustrated with the 2D correlated model, from which their associated indexes for the canonical ensemble of a pair of interacting harmonic oscillators, are obtained.