  The glass transition refers to the non-equilibrium process by which an
equilibrium liquid is transformed to a non-equilibrium disordered solid, or
vice versa. Associated response functions, such as heat capacities, are
markedly different on cooling than on heating, and the response to melting a
glass depends markedly on the cooling protocol by which the glass was formed.
This paper shows how this irreversible behavior can be interpreted
quantitatively in terms of an East-model picture of localized excitations (or
soft spots) in which molecules can move with a specific direction, and from
which excitations with the same directionality of motion can appear or
disappear in adjacent regions. As a result of this facilitated dynamics,
excitations become correlated in a hierarchical fashion. These correlations are
manifested in the dynamic heterogeneity of the supercooled liquid phase. While
equilibrium thermodynamics is virtually featureless, a non-equilibrium glass
phase emerges when the model is driven out of equilibrium with a finite cooling
rate. The correlation length of this emergent phase is large and increases with
decreasing cooling rate. A spatially and temporally resolved fictive
temperature encodes memory of its preparation. Parameters characterizing the
model can be determined from reversible transport data, and with these
parameters, predictions of the model agree well with irreversible differential
scanning calorimetry.
