Many-body Brownian ratchets and active memories

Systems driven out of equilibrium can realize phenomena forbidden in equilibrium, such as robust information storage. Yet it is often unclear how to realize a given set of abstract dynamics in a physically natural driven system. In this talk, I show how to simulate any local active dynamics with a many-body Brownian ratchet: a bilayer system whose two layers are coupled to baths at different temperatures. Applying this construction to Toom's rule, I construct a nearest-neighbor Ising model whose ferromagnetic phase is stable to symmetry-breaking perturbations. Finally, I show that a related construction, sliding two Ising models against each other, yields an ordered state with a very long lifetime in one dimension.