Using atomistic simulations and metrics from statistical mechanics we show that the oxygen anions in UO2 predominantly hop from one native (tetrahedral) lattice site to another, above a characteristic temperature Tα (~2000 K). Interestingly, we discover two types of disorder-the first one, which is a measure of the fraction of anions that are displaced from their native sites, portrays a monotonic increase with temperature and shows excellent conformity to neutron scattering data. The second metric demonstrates a dynamic clustering or self-organization behavior wherein the anions are spatially correlated to those with similar mobility. The dynamic self-organization, however, experiences a non-monotonic variation with temperature depicting a maximum near the Bredig or λ-transition. We further establish that the thermodynamic metric cp/T, which is equal to the rate of change of entropy with temperature, is a key thermodynamic indicator of the dynamic disorder among the oxygen anions.