Again, define  and  to be conjugate pairs, and the  to be the natural variables of some potential .  We may take the "cross differentials" of the state equations,  which obey the following relationship:
From these we get the Maxwell relations. There will be  of them for each potential giving a total of  equations in all. If we restrict ourselves the , , , 
Using the equations of state involving the chemical potential we get equations such as:
and using the other potentials we can get equations such as: