  Kinetically constrained models (KCM) generically have trivial thermodynamics
and yet manifest rich glassy dynamics. In order to resolve the
thermodynamics-dynamics disconnect in KCMs, we derive a KCM by coarse-graining
a non-trivial thermodynamic model with a solvable partition function. Blending
of thermodynamics to the KCM makes the role of landscape properties on the
relaxation times, fragility and its crossover analytically transparent. Using
Bethe ansatz, we calculate the time-dependent $N$-point probability function in
the distinct dynamical regimes of the landscapes; the contribution of the
glassy term is identified.
