Universality classes for the Fisher metric derived from relative group entropy

GOMEZ, IGNACIO S.; PORTESI, M.; BORGES, ERNESTO P.

PHYSICA A - STATISTICAL AND THEORETICAL PHYSICS

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2020 vol. 547 p. 12382701 - 12382713

0378-4371

We consider the Fisher metric which results from the Hessian of the relative group entropy, that we call group Fisher metric. In particular, the metrics corresponding to the Boltzmann-Gibbs, Tsallis, Kaniadakis and Abe universality classes are obtained. We prove that the scalar curvature derived from the group Fisher metric results in a multiple of the Boltzmann-Gibbs one, with the factor of proportionality given by the local properties of the group entropy. We analyse, for the Tsallis universality class, the 2D correlated model that presents a softening and strengthening of the scalar curvature, and we illustrate with the canonical ensemble of a pair of interacting harmonic oscillators as well as a quartic harmonic oscillator.