  Cosmological boundary conditions for particles and fields are often discussed
as a Cauchy problem, in which configurations and conjugate momenta are
specified on an "initial" time slice. But this is not the only way to specify
boundary conditions, and indeed in action-principle formulations we often
specify configurations at two times and consider trajectories joining them.
Here, we consider a classical system of particles interacting with short range
two body interactions, with boundary conditions on the particles' positions for
an initial and a final time. For a large number of particles that are randomly
arranged into a dilute gas, we find that a typical system trajectory will
spontaneously collapse into a small region of space, close to the maximum
density that is obtainable, before expanding out again. If generalizable, this
has important implications for the cosmological arrow of time, potentially
allowing a scenario in which both boundary conditions are generic and also a
low-entropy state "initial" state of the universe naturally occurs.
