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.