Information Geometry on the \(\kappa\)-Thermostatistics

Abstract

We explore the information geometric structure of the statistical manifold generated by the \(\kappa\)-deformed exponential family. The dually-flat manifold is obtained as a dualistic Hessian structure by introducing suitable generalization of the Fisher metric and affine connections. As a byproduct, we obtain the fluctuation-response relations in the \(\kappa\)-formalism based on the \(\kappa\)-generalized exponential family.

Keywords

• \(\kappa\)-entropy
• \(\kappa\)-exponential
• \(\kappa\)-logarithm
• information geometry
• Fisher metric
• dually-flat
• fluctuation-response relation