The high-density population maxima are indicated on top of the potential energy profile in Figure , which reveals a different behavior than the population profile; the potential energy minima do not match with the population maxima. Rather, the high densities are found around the potential energy minima, possibly because of the entropic effect. For instance, two potential energy minima per layer per unit cell are identified, whereas four Na + ions are available. Thus, the sodium ions cannot occupy the energetically favorable sharp potential energy regions (-2.4 eV), but rather occupy the sites which are greater in number and therefore higher in entropy. The difference between the effects of energy and entropy can be linked through Eq. 8, in which entropy plays a significant role. Specifically, particles usually avoid energetically favorable sharp potential energy minima with low entropy, whereas they prefer a relatively higher energy basin which has high entropy. This scenario can be understood by implementing a simulation which places fewer Na + ions in a conducting layer (detailed in the METHODOLOGY section IV). The Na + ion density pattern and the potential energy profile are shown in Figure in the supplementary information for the under-loaded conduction plane. In the potential energy profile, the locations of the potential energy minima are almost unchanged, whereas the population density pattern changes significantly. Only one type of ring exists, consisting of four high-density maxima. The highest population densities are identified exactly at the potential minima. In this case, the smaller number of Na + ions contributes to a lower entropy, resulting in an energy-driven population distribution. The entropy contribution is even lower if the number of Na + ions in the conduction layer is reduced even further, as shown in Figure , where all population density maxima and potential minima coincide exactly in the conduction plane, implying a minimal entropic contribution. For a quantitative estimation of the intra-and interring free energy barrier heights that determine the Na + ion diffusion mechanism, the one-dimensional free energy distributions among the high-density population maxima are shown in Figure . The free energies were calculated by counting the population density distributions inside a rectangle connecting two high-density areas (with a width of 1.0 Å) as indicated in Figure and projected along a straight line connecting two sites using Eq. 9. Figure captures the free energy minima and maxima for inter and intra-ring cases, distinctly, as reflected in Figure . The pairs of site distances and corresponding free energy barriers of Na + ion hopping are listed in Table II. The inter-ring free energy barriers are higher than the intra-ring free energy barriers, which is also reflected in Figure . Thus, the intra-ring mechanism is more favorable than the inter-ring mechanism. However, both mechanisms are responsible for the long-range Na + ion diffusion. A direct ring mechanism is also revealed by randomly tracking a Na + ion over simulation time, as displayed in Figure , where the high-density Na sites (S1, S2, and S3) are also marked. The Na + ions diffuse through both the inter-ring and intra-ring pathways, as evident in the free energy barriers and the population density profiles.