Growth kinetics and thermodynamic equilibrium can both be determining factors at different stages of III-V semiconductor heteroepitaxy. We study their interplay, employing kinetic Monte Carlo simulations for the InAs(001) surface. The simulation contains atomistic details of both species, including the stability of different reconstructions and their kinetics. The behavior of the surface in thermodynamic equilibrium, including different reconstructions, is determined exclusively by extensive total energy calculations employing ab initio density functional theory. The continuous phase transition between the α?(2×4) and β?(2×4), predicted by theory, is confirmed by experiment. At full layer coverage, a recovery of the stable reconstruction is observed. The different time scales associated with As2 and In are discussed with respect to equilibrium and kinetics.