The surfaces of clay minerals, which are abundant in atmospheric mineral dust, serve as an important medium to catalyze ice nucleation. The lateral edge surface of 2:1 clay minerals is postulated to be a potential site for ice nucleation. However, experimental investigations of the edge surface structure itself have been limited compared to the basal planes of clay minerals. Density functional theory (DFT) computational studies have provided insights into the pyrophyllite edge surface. Pyrophyllite is an ideal surrogate mineral for the edge surfaces of 2:1 clay minerals as it possesses no or little structural charge. Of the two most-common hydrated edge surfaces, the AC edge, (110) surface in the monoclinic polytype notation, is predicted to be more stable than the B edge, (010) surface. These stabilities, however, were determined based on the total energies calculated at 0K and did not consider environmental effects such as temperature and humidity. In this study, atomistic thermodynamics based on periodic DFT electronic calculations was applied to examine the effects of environmental variables on the structure and thermodynamic stability of the common edge surfaces in equilibrium with bulk pyrophyllite and water vapor. We demonstrate that the temperature-dependent vibrational energy of sorbed water molecules at the edge surface is a significant component of the surface free energy and cannot be neglected when determining the surface stability of pyrophyllite. The surface free energies were calculated as a function of temperature from 240 to 600K and water chemical potential corresponding to conditions from ultrahigh vacuum to the saturation vapor pressure of water. We show that at lower water chemical potentials (dry conditions), the AC and B edge surfaces possessed similar stabilities; at higher chemical potentials (humid conditions) the AC edge surface was more stable than the B edge surface. At high temperatures, both surfaces showed similar stabilities regardless of the water chemical potential. The equilibrium morphology of pyrophyllite crystals is also expected to be dependent on these two environmental variables. Surface defects may impact the surface reactivity. We discuss the thermodynamic stability of a possible Si cation vacancy defect which provides additional hydroxyl group on the surface.