Monte Carlo techniques are used to simulate the thermodynamics and diffusion of Li in the intercalation compound LiyMn2O4.. Results are presented for stoichiometric LiyMn2O4 and for Li-rich LiyMn2O4 containing pinned Li. The predicted theoretical open-circuit potential compares favorably with literature results. The influence of Li-Li interactions on the activation energy leads to a diffusion coefficient that depends upon concentration. The diffusion coefficient is interpreted in terms of a thermodynamic factor and a binary interaction parameter.