  Information geometry is an emergent branch of probability theory that
consists of assigning a Riemannian differential geometry structure to the space
of probability distributions. We present an information geometric investigation
of gases following the Fermi-Dirac and the Bose-Einstein quantum statistics.
For each quantum gas, we study the information geometry of the curved
statistical manifolds associated with the grand canonical ensemble. The
Fisher-Rao information metric and the scalar curvature are computed for both
fermionic and bosonic models of non-interacting particles. In particular, by
taking into account the ground state of the ideal bosonic gas in our
information geometric analysis, we find that the singular behavior of the
scalar curvature in the condensation region disappears. This is a
counterexample to a long held conjecture that curvature always diverges in
phase transitions.
