Vacuum structure and the arrow of time

We find ourselves in an extended era of entropy production. Unlike most other observations, the arrow of time is usually regarded as a constraint on initial conditions. I argue, however, that it primarily constrains the vacuum structure of the theory. I exhibit simple scalar field potentials in which low-entropy initial conditions are not necessary, or not sufficient, for an arrow of time to arise. In particular, in some models an arrow of time obtains even if the initial vacuum has arbitrarily large entropy. In such examples, the dynamical resolution of the arrow of time problem arises from properties of the vacuum structure similar to those that allow the string landscape to solve the cosmological constant problem without producing an empty universe, particularly its high dimensionality and the large difference in vacuum energy between neighboring vacua.