  The Fredkin spin chain serves as an interesting theoretical example of a
quantum Hamiltonian whose ground state exhibits a phase transition between
three distinct phases, one of which violates the area law. Here we consider a
classical stochastic version of the Fredkin model, which can be thought of as a
simple exclusion process subject to additional kinetic constraints, and study
its classical stochastic dynamics. The ground state phase transition of the
quantum chain implies an equilibrium phase transition in the stochastic
problem, whose properties we quantify in terms of numerical matrix product
states (MPS). The stochastic model displays slow dynamics, including power law
decaying autocorrelation functions and hierarchical relaxation processes due to
exponential localization. Like in other kinetically constrained models, the
Fredkin chain has a rich structure in its dynamical large deviations - which we
compute accurately via numerical MPS - including an active-inactive phase
transition, and a hierarchy of trajectory phases connected to particular
equilibrium states of the model. We also propose, via its height field
representation, a generalization of the Fredkin model to two dimensions in
terms of constrained dimer coverings of the honeycomb lattice.
