  The effects of floppy modes in the thermodynamical properties of a system are
studied. From thermodynamical arguments, we deduce that floppy modes are not at
zero frequency and thus a modified Debye model is used to take into account
this effect. The model predicts a deviation from the Debye law at low
temperatures. Then, the connection between the topography of the energy
landscape, the topology of the phase space and the rigidity of a glass is
explored. As a result, we relate the number of constraints and floppy modes
with the statistics of the landscape. We apply these ideas to a simple model
for which we provide an approximate expression for the number of energy basins
as a function of the rigidity. This allows to understand certains features of
the glass transition, like the jump in the specific heat or the reversible
window observed in chalcogenide glasses.
