The Mpemba effect (ME) is investigated in the context of ubiquitous quantum oscillators and two-level systems (TLS) using a novel approach. Exact reduced density matrices for various initial states are derived. The temporal behavior of the trace distance for these initial states is calculated analytically and presented. For a dissipative quantum oscillating system, it is demonstrated that number states |𝑁⟩ intersect with coherent states |𝛼⟩, with this intersection occurring earlier for smaller values of 𝑁. Additionally, thermal states intersect with coherent states for specific values of |𝛼|, leading to the occurrence of the ME in these two scenarios. A weaker version of the ME is also observed for thermal and number states. In the case of a quantum TLS, it is shown that the ME occurs, and the potential for its experimental observation is discussed, with reference to the Jaynes-Cummings model (JCM) involving a time-dependent coupling function.
