On the trail of the 2-body reduced density matrix

A brief review is made of developments in the theory of reduced density matrix estimation of fermion system properties, to which John Coleman contributed enormously. Emphasis is placed upon those constraints that are peculiar to the system in question, as well as to those of “universal” validity. The former are typically obtained by following the consequences of the insertion or deletion of one of the particles of the system, and, for example, the PY equation of classical fluid theory is identified as the “saturation” of a valid inequality. An analogous process for fermion systems is introduced but not carried out very far.