where ⟨• • • ⟩ R N ,Ω N denotes an average over FG configurations that are mapped to CG configuration (R N , Ω N ). The left-hand side of Eq. ( ) consists of a product of separate factors for each CG particle that do not depend on the configuration of the CG system, whereas the right-hand side in general is not separable into independent factors and does depend on the CG configuration. Consistency between FG and CG angular momenta requires the right-hand side of Eq. ( ) to be separable into independent factors for each principal axis of each CG particle, which should be achievable (at least approximately) via a judicious choice of the CG mapping, e.g. by mapping groups of FG particles that form approximately rigid bodies into CG particles such that the inertia tensor I I I FG,I of each group of FG particles is largely unperturbed by the surrounding particles. In this case, from Eq. ( ) the consistency condition for the angular momentum about the principal axis q of CG particle I is