Molecular distribution functions in the grand canonical ensemble

6 Molecular distribution functions in the grand canonical ensemble 

In the previous section, we introduced the MDF in the canonical ensemble, i.e., the MDF in a closed system with fixed values of T, V, N. Similarly, one can define the MDF in any other ensemble, such as the T, P, N ensemble. Of particular interest, for this book, are the MDFs in the grand canonical ensemble, i.e., the MDF pertaining to an open system characterized by the variables T, V, /i. The fundamental probability in the grand canonical ensemble is 

The conditional nth-order MDF of finding the configuration X given that the system has N particles, is  

The bar over p(n (XN) denotes the average in the T, V, p ensemble. Recalling that the canonical partition function is 

The normalization condition for p n (Xn) is obtained from (2.76) by integrating over all the configurations Xn  

---

MOLECULAR DISTRIBUTION FUNCTIONS IN THE GRAND CANONICAL ENSEMBLE... 

---