It is most illuminating to understand the SP formula in the context of the DLD model, which describes motion in dynamical disorder. In order to derive the dephasing rate formula from first principles, a purity-based definition of the dephasing factor can be adopted. The purity P ( t ) = e − − F ( t ) describes how a quantum state becomes mixed due to the entanglement of the system with the environment. Using perturbation theory, one recovers at finite temperatures at the long time limit F ( t ) = Γ Γ φ φ t , where the decay constant is given by the dephasing rate formula with non symmetrized spectral functions as expected. There is a somewhat controversial possibility to get power law decay of P ( t ) at the limit of zero temperature. The proper way to incorporate Pauli blocking in the many-body dephasing calculation, within the framework of the SP formula approach, has been clarified as well.