  Searching for the ideal glass transition, we exploit the ability of glassy
polymer films to explore low energy states in remarkably short time scales. We
use 30 nm thick polystyrene (PS) films, which in the supercooled state
basically display the bulk polymer equilibrium thermodynamics and dynamics. We
show that in the glassy state, this system exhibits two mechanisms of
equilibrium recovery. The faster one, active well below the kinetic glass
transition temperature ($T_g$), allows massive enthalpy recovery. This implies
that the 'fictive' temperature ($T_f$) reaches values as low as the predicted
Kauzmann temperature ($T_K$) for PS. Once the thermodynamic state corresponding
to $T_f = T_K$ is reached, no further decrease of enthalpy is observed. This is
interpreted as a signature of the ideal glass transition.
