We used molecular dynamics simulation to investigate the friction of a single asperity against a rigid substrate, while generating debris. In the low wear regime (i.e., non-linear wear rate dependence on the contact stress, via atom-by-atom attrition), the frictional stress is linearly dependent on the normal stress, without any lubrication effect from the wear debris particles. Both the slope (friction coefficient) and friction at zero normal stress depend strongly on asperity-substrate adhesion. In the high wear regime (i.e., linear wear rate dependence on the contact stress, via plastic flow), the friction-normal stress curves deviate from a linear relation merging toward plastic flow of the single asperity which is independent of the interfacial adhesion. One can further link wear and friction by considering debris generation as chemical reaction, driven by both normal and frictional forces. The coupling between wear and friction can then be quantified by a thermodynamic efficiency of the debris generation. While the efficiency is less than 5% in the low wear regime, indicating poor mechanochemical coupling, it increases with normal stress toward 50% in the high wear regime.