Non-equilibrium dynamics of exactly solvable cellular automata

In both classical and quantum non-equilibrium there is currently much interest in systems with constrained dynamics. I will consider one class of such problems, that of deterministic classical cellular automata, specifically the so-called Rules 54, 201 and 150 CAs. These correspond to discrete time and deterministic counterparts of stochastic lattice systems often studied in the context of glasses or of Rydberg atoms, specifically the Fredrickson-Andersen, the PXP, and the XOR-FA kinetically constrained models. I will show how these CAs are integrable and how many properties of their dynamics can be computed exactly using matrix product states, including non-equilibrium steady
states, time-correlators and dynamical large deviations.