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On the example of a mean-field Fredrickson-Andersen kinetically constrainedmodel, we focus on the known property that equilibrium dynamics take place at afirst-order dynamical phase transition point in the space of time-realizations.We investigate the finite-size properties of this first order transition. Bydiscussing and exploiting a mapping of the classical dynamical transition -anargued glassiness signature- to a first-order quantum transition, we show thatthe quantum analogy can be exploited to extract finite-size properties, whichin many respects are similar to those in genuine mean-field quantum systemswith a first-order transition. We fully characterize the finite-size propertiesof the order parameter across the first order transition.

Finite size effects in a mean-field kinetically constrained model: dynamical glassiness and quantum criticality