Finally, in Fig. , we present a further comparison of the polariton relaxation dynamics computed using the spin-PLDM approach 69,70 for model 1. The theoretical details of this approach can be found in Ref. 69. Similar to the original PLDM approach, spin-PLDM explicitly accounts for the forward and backward propagators of the quantum subsystem, using the forward and backward mapping variables. One can see in Fig. that spin-PLDM provides more accurate results compared to spin-LSC and achieves an accuracy at a similar level of γ-SQC (see Fig. ). However, being a partially forward and backward method, the computational cost of spin-PLDM is significantly increased compared to the Ehrenfest method and all linearized mapping approaches (γ-SQC and spin-LSC).