The fact that the fundamental equation applies to both reversible and irreversible
changes may be puzzling at first sight. The reason is that only in the case of a reversible
change may TdS be identified with dq and −pdV with dw. When the change is
irreversible, TdS > dq (the Clausius inequality) and −pdV > dw. The sum of dw and dq
remains equal to the sum of TdS and −pdV, provided the composition is constant.