  As highly tunable interacting systems, cold atoms in optical lattices are
ideal to realize and observe negative absolute temperatures, T < 0. We show
theoretically that by reversing the confining potential, stable superfluid
condensates at finite momentum and T < 0 can be created with low entropy
production for attractive bosons. They may serve as `smoking gun' signatures of
equilibrated T < 0. For fermions, we analyze the time scales needed to
equilibrate to T < 0. For moderate interactions, the equilibration time is
proportional to the square of the radius of the cloud and grows with increasing
interaction strengths as atoms and energy are transported by diffusive
processes.
