  The principal theme of this paper is that anomalously slow, super-Arrhenius
relaxations in glassy materials may be activated processes involving chains of
molecular displacements. As pointed out in a preceding paper with A. Lemaitre,
the entropy of critically long excitation chains can enable them to grow
without bound, thus activating stable thermal fluctuations in the local density
or molecular coordination of the material. I argue here that the intrinsic
molecular-scale disorder in a glass plays an essential role in determining the
activation rate for such chains, and show that a simple disorder-related
correction to the earlier theory recovers the Vogel-Fulcher law in three
dimensions. A key feature of this theory is that the spatial extent of
critically long excitation chains diverges at the Vogel-Fulcher temperature. I
speculate that this diverging length scale implies that, as the temperature
decreases, increasingly large regions of the system become frozen and do not
contribute to the configurational entropy, and thus ergodicity is partially
broken in the super-Arrhenius region above the Kauzmann temperature $T_K$. This
partially broken ergodicity seems to explain the vanishing entropy at $T_K$ and
other observed relations between dynamics and thermodynamics at the glass
transition.
