Relations between Thermodynamic Quantities and GMDFs

In this section, we present some formal relations between thermodynamic quantities and GMDF s. We elaborate on some simple examples here, and defer to Section 5.8 the discussion of more general relations. 

Two quite obvious connections follow almost directly from the definitions  

This example seems to be representative of a general result When a given quantity is expressed in terms of GMDF s, it requires in general a lower-order distribution function compared with the corresponding expression in terms of ordinary MDF s. We shall encounter other examples later. It should be realized that although the GMDF s may seem to be more complex than ordinary MDF s, this does not necessarily imply that their computation, either analytically or numerically, should be more difficult. 

The second relation (5.46) is obvious and follows from the fact that the volumes of the VP of all particles add up to give the total volume of the system. [In the T, F, N ensemble, (5.46) gives the exact volume V of the system. On the other hand, in the T, P, N ensemble, V stands for the average volume of the system.] 

We now discuss various derivatives of E and V that will be useful in later applications. 

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