  In the article, we investigate entanglement dynamics defined by
time-dependent linear generators. We consider multilevel quantum systems
coupled to an environment that induces decoherence and dissipation, such that
the relaxation rates depend on time. By applying the condition of partial
commutativity, one can precisely describe the dynamics of selected subsystems.
More specifically, we investigate the dynamics of entangled states. The
concurrence is used to quantify the amount of two-qubit entanglement in the
time domain. The framework appears an efficient tool for investigating quantum
evolution of entangled states driven by time-local generators. In particular,
non-Markovian effects can be included to observe the restoration of
entanglement in time.
