This is called Poincaré recurrence. If you have an infinite amount of time to work with, any state the system can be in is a state it WILL be in again, an infinite number of times, with a recurrence time determined by how rare or special that configuration is. In one rather arresting example, physicists Anthony Aguirre, Sean Carroll, and Matthew Johnson once calculated that if you were willing to wait something like a trillion trillion times the age of the universe, you could watch an entire piano spontaneously assemble itself in a seemingly empty box.
