If the Ehrenfest+R method has been successful, this sum in Eq. B6 should be equivalent to the Lindblad Liouvillian in Eq. A5. The k Eh + k R and -k Eh -k R elements in the right-hand column of Eq. B6 match the elements inside the Lindblad Liouvillian L (Eq. A5), Γ and -Γ, respectively, due to Eq. A22a. The elements in the middle two columns of Eq. B6 require closer inspection. The expectation value inside of α can be evaluated as