  Freestanding thin polymer films with high molecular weights exhibit an
anomalous decrease in the glass-transition temperature with film thickness.
Specifically, in such materials, the measured glass-transition temperature
evolves in an affine way with the film thickness, with a slope that weakly
depends on the molecular weight. De Gennes proposed a sliding mechanism as the
hypothetical dominant relaxation process in these systems, where stress kinks
could propagate in a reptation-like fashion through so called bridges, i.e.
from one free interface to the other along the backbones of polymer
macromolecules. Here, by considering the exact statistics of finite-sized
random walks within a confined box, we investigate in details the bridge
hypothesis. We show that the sliding mechanism cannot reproduce the basic
features appearing in the experiments, and we exhibit the fundamental reasons
behind such a fact.
