  We derive the multiparticle-correlation expansion of the excess entropy of
classical particles in the canonical ensemble using a new approach that
elucidates the rationale behind each term in the expansion. This formula
provides the theoretical framework for an entropy-based ordering criterion that
has been already tested for a variety of model fluids and thermodynamic
phenomena. In view of future investigations of the phase diagram of colloidal
mixtures, we detail in this paper the case of a two-component system of
spherical and rod-like particles and discuss the symmetries underlying both the
self and distinct pair-distribution functions under various geometrical
constraints.
