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Kinetically constrained models (KCMs) were introduced by physicists to modelthe liquid-glass transition. They are interacting particle systems on$\mathbb{Z}^d$ in which each element of $\mathbb{Z}^d$ can be in state 0 or 1and tries to update its state to 0 at rate $q$ and to 1 at rate $1-q$, providedthat a constraint is satisfied. In this article, we prove the firstnon-perturbative result of convergence to equilibrium for KCMs with generalconstraints: for any KCM in the class termed "supercritical" in dimension 1 and2, when the initial configuration has product $\mathrm{Bernoulli}(1-q')$ lawwith $q' \neq q$, the dynamics converges to equilibrium with exponential speedwhen $q$ is close enough to 1, which corresponds to the high temperatureregime.

Exponential convergence to equilibrium in supercritical kinetically constrained models at high temperature