Similar to the fraction of mobile ions (Eq. 2), only a relatively small fraction of all phonon occupation fluctuations can result in an ionic jump, even if multiple modes participate in the fluctuation. When calculating the probability that a fluctuation is large enough for ionic transport (see Supplemental Information 6) it is significantly lower (blue area in Figure ) than, for example, the probability that a fluctuation is within one standard deviation of the equilibrium phonon occupation number (red area in Figure ). Since the standard deviation of an exponential distribution is equal to its average value, it follows that the majority of phonon fluctuations are within the bounds 0 ≤ ≤ 2 , and ≈ 5.0 phonons for Ag + vibrational modes near room temperature. From this perspective it is not surprising that thermal transport is independent of the activation barrier or ionic transport (Figure ) since thermal transport is dominated primarily by average phonon fluctuations.