Analytical theories for lattice adsorption and diffusion recently published are tested with molecular dynamics (MD) simulations. Our analytical theories are generalized and can be applied to various small molecules in different nanoporous structures such as zeolites and molecular sieves. In this work, we validate our theory by comparing the results with those predicted by simulations. We study the behavior of methane in zeolite Na-Y. Specifically, the MD simulations are conducted to obtain the interaction energies and self-diffusion coefficients at five different temperatures and loadings. While the lattice adsorption theory incorporates minimum parameters to obtain the thermodynamic properties, the diffusion component of the theory incorporates no adjustable parameters. Our theory is in very good qualitative agreement with the simulations. Overall, reasonably good quantitative agreement is found between the theory and simulations. Our theory studies the effect of temperature and density on the adsorption and diffusion of methane in Na-Y. Our theory requires approximately only a minute to obtain the results, as compared with the tens of CPU hours required for simulations.