Track linear and angular velocity (I have read papers that discuss tracking total kinetic energy. Tracking velocity is simpler). When both are below thresholds, decrement a counter (else set the counter to a predefined max value). When the counter reaches zero, remove the active object from the active list (and place on the inactive/static list). This counter style requires a fixed deltaTime integrator.

Waking sleeping stacked/touching objects is more complicated. Tracking broken contacts or examining nearby objects during wakeup is required (otherwise, a lower object can be pushed from a stack and the upper objects will not wake up. Similar concept for leaning objects). Thresholds can also be used to keep slight perturbations from waking sleeping objects.