At a deeper level, the difference between ionic and thermal transport is better understood by considering their similarities, that is the microscopic origin of both processes: phonon occupation fluctuations. Thermal transport in solids arises from any deviation ( -) ≠ 0 from the equilibrium phonon occupation number , with being the instantaneous occupation of mode N (see Supplemental Note 6). Only the drift velocity of the phonon (e.g., phonon-gaslike or diffuson-like) determines the magnitude of its contribution to transport. In contrast, ionic motion is an activated process such that a critical fluctuation has to be reached for the ion to overcome the activation barrier. The magnitude of this critical fluctuation will depend on the vibrational mode(s) involved and the specific jump that is considered (for example see Figure ). For a single vibrational mode that oscillates in the jump direction, the critical number of phonons O required for a jump to occur is