A theoretical investigation of the behavior of atomic friction at low temperatures is performed using a master equation method with a two-mass, two-spring Prandtl-Tomlinson model of an atomic force microscope experiment. A novel approach is taken in which two distinct instability mechanisms are introduced into the model: thermal activation is described by transition state theory with a prefactor associated with the frequency of the tip apex, and athermal instability is introduced by an Arrhenius-like equation with a prefactor associated with the characteristic frequency of the cantilever. Thermal instability causes the often reported decrease of friction with temperature followed by a stable low-friction region at high temperatures. However, the introduction of the athermal term that describes other instability mechanisms extends the predictive capability of the model such that it captures the friction plateau observed at very low temperatures.