Temporal fluctuations about the long-time average will be small so long as the off-diagonal elements satisfy the conditions imposed on them by the ETH, namely that they become exponentially small in the system size. Notice that this condition allows for the possibility of isolated resurgence times, in which the phases align coherently in order to produce large fluctuations away from the long-time average. The amount of time the system spends far away from the long-time average is guaranteed to be small so long as the above mean squared amplitude is sufficiently small. If a system poses a dynamical symmetry, however, it will periodically oscillate around the long-time average.