As noted earlier, the quantity 
is a measure of the instantaneous value of
the internal pressure 
. Let us look at the ensemble average
of this quantity
Doing the volume integration by parts gives
Thus,
This result is known as the pressure virial theorem. It illustrates that
the average of the quantity gives the fixed
pressure P that defines the ensemble.
Another important result comes from considering the ensemble average
Once again, integrating by parts with respect to the volume yields
or
This result is known as the work virial theorem. It expresses the fact that equipartitioning of energy also applies to the volume degrees of freedom, since the volume is now a fluctuating quantity.