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Dually Flat Geometries in the State Space of Statistical Models
1  Universiteit Antwerpen, Belgium


This paper investigates whether the dually flat geometries introduced by Amari are useful as a tool to study the manifold of thermodynamic equilibrium states. The mathematical setting is that of statistical models belonging to an exponential family. The metric tensor is derived from the relative entropy. Flat geometries are introduced and thermodynamic length is calculated. The ideal gas serves as an example.

Keywords: information geometry; dually flat geometries; thermodynamic length; exponential family; relative entropy; ideal gas