Chain relations of reduced distribution functions and their associated correlation functions

For a closed system, the integration (trace in the quantum case) over one particle of a reduced distribution function is related to the reduced distribution function of one lower order, The particular details of this "chain" relation depend sensitively on the detailed manner in which the reduced distribution functions are defined, specifically their normalization. Correlation functions are defined in terms of reduced distribution functions, which fixes the normalization of the correlation functions and, provided they exist, their associated chain relations. Chain relations for the correlation functions are shown to exist for normalizations of generic type but not for normalizations of specific type. The normalization requirement is shown, in general, to prevent the direct association of correlation functions with physical clusters, which is commonly assumed in the literature, These relations are illustrated for an ideal gas of monomers and dimers. The effect of taking the thermodynamic limit on the chain relations for this system is discussed. This illustrates how the thermodynamic limit generally destroys the chain relations. (C) 1998 American Institute of Physics.