  Geometry of hypersurfaces defined by the relation which generalizes classical
formula for free energy in terms of microstates is studied. Induced metric,
Riemann curvature tensor, Gauss-Kronecker curvature and associated entropy are
calculated. Special class of ideal statistical hypersurfaces is analyzed in
details. Non-ideal hypersurfaces and their singularities similar to those of
the phase transitions are considered. Tropical limit of statistical
hypersurfaces and double scaling tropical limit are discussed too.
