with H s expressed in Eq. 86, and the nuclear DOFs obeys Eq. 98a-Eq. 98b. Thus, we have discovered conjugate variables {Θ n , ϕ n } which decompose the N 2 -1 coupled equations in Eq. 98c into 2N -2 coupled equations. In fact, Θ n and ϕ n play a similar role as the "action" and the "angle" variables in the original Meyer-Miller mapping formalism. 9 This is not very surprising, as the action variables are related to the population of states, and Θ n is directly related to the population estimator (see Eq. 75) and thus related to the action variable (Eq. 122) as well.