Information-geometric structures derived from group relative entropies

BORGES, ERNESTO P.; GÓMEZ, I.S.; PORTESI, M.

Ciudad Autónoma de Buenos Aires

Conferencia; StatPhys27; 2019

Departamento de Física, FCEyN, UBA

Based on the notion of group relative entropy, we derive the associated Fisher metric from a geometrical point of view. In particular we consider the Boltzmann-Gibbs, Tsallis, Kaniadakis and Abe classes. Our study reveals that the group Fisher metric is a tool for characterizing statistical models in various aspects: generalization of Fisher information measures and complexities associated with group entropies, connection between correlated and uncorrelated models, link of global geometric indicators with macroscopic quantities. We illustrate these features with the canonical ensemble of a pair of interacting harmonic oscillators.