Fundamentally, thermal and ionic transport are related at the vibrational level as they both arise from fluctuations of the phonon occupation number , which is the instantaneous number of vibrations (phonon quanta) that are in a vibrational mode having frequency . Thermal transport results from the thermodynamic drive to have a constant phonon occupation (thermal energy) throughout the entire material. Ion transport occurs when a thermal fluctuation is energetically capable of moving the ion between adjacent lattice sites.