GaN (0001) surface in an ammonia-rich vapor ambient, typical for ammonia annealing, metalo-organic vapor phase epitaxy (MOVPE) or hydride vapor phase epitaxy (HVPE) was considered. It was shown that, in these three cases, the stationary state of the surface corresponds to condition far from equilibrium. The chemical potential of nitrogen and hydrogen at the surface was determined using kinetic arguments, i.e., derived form the magnitude of flux of ammonia. For HVPE and MOVPE growth, the chemical potential of gallium depends on the distance from the steps. Thus, only far distance from the step value of the gallium chemical potential at the GaN(0001) surface could be determined in similar way. In the alternative case of GaN annealing in ammonia atmosphere, gallium chemical potential at the surface remains undetermined (the surface is in a metastable state). Additionally, using thermodynamic arguments, the limits for the chemical potential of gallium (upper) and nitrogen (lower) were formulated for the case of vapor growth, and expressed as functions of temperature and pressure. The results, regarding the atomic processes on the GaN(0001) surface, were obtained using the SIESTA, density functional theory based code, and consequently employed in the comparable thermodynamic and kinetic analysis of the state of GaN(0001) surface.