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. I argue that the string theory landscape gives rise to an arrow of time independently of the initial entropy, assuming a plausible condition on the lifetime of its metastable vacua. The dynamical resolution of the arrow of time problem arises from the same structural properties of the string landscape that allow it 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.