The dynamics of the projected state P ρ ρ , under any idempotent projection operator (where P 2 = P ), is described by the NZ generalized master equation (GQME). This equation can be used to obtain a closed equation of motion for the reduced system dynamics, focusing solely on the dynamics within the subsystem of interest. d d t P ρ ρ ^ ^ ( t ) = − − i ℏ ℏ P L P ρ ρ ^ ^ ( t ) − − i ℏ ℏ 2 ∫ ∫ 0 t d τ τ P L e − − i Q L τ τ / ℏ ℏ Q L P ρ ρ ^ ^ ( t − − τ τ ) − − i ℏ ℏ P L e − − i Q L τ τ / ℏ ℏ Q ρ ρ ^ ^ ( 0 )