Exact relaxation to Gibbs and non-equilibrium steady states in the quantum cellular automaton Rule 54

We study the out-of-equilibrium dynamics of quantum cellular automaton Rule 54 using a time-channel approach. exhibit family (non-equilibrium) product states for which we are able to describe exactly full relaxation dynamics. use this prove that finite subsystems relax one-parameter Gibbs states. also consider inhomogeneous quenches. Specifically, show when two halves system prepared in different solvable states, at distance from centre eventually non-equilibrium steady state (NESS) predicted by generalised hydrodynamics. To best our knowledge, is first exact description NESS an interacting and, therefore, independent confirmation hydrodynamics quench.