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We review recent developments in structural-dynamical phase transitions intrajectory space. An open question is how the dynamic facilitation theory ofthe glass transition may be reconciled with thermodynamic theories that posit avanishing configurational entropy. Dynamic facilitation theory invokes adynamical phase transition, between an active phase (close to the normalliquid) and an inactive phase which is glassy, whose order parameter is eitherdynamic or a time-averaged structural quantity. In particular, the dynamicalphase transition in systems with non-trivial thermodynamics manifestssignatures of a lower critical point, which lies close to the putative Kauzmanntemperature, where any thermodynamic phase transition to an ideal glass statemight occur. We discuss these findings, and suggest that the lower criticalpoint of the structural-dynamical phase transition may be related to the largedrop in configurational entropy that occurs in the inactive phase of thedynamical phase transition. Increasing supercooling thus brings configurationalentropy of the normal liquid much lower, along with the temperature.

Dynamical Phase Transitions and their Relation to Thermodynamic Glass Physics