Indivisible quantum evolution of a driven open spin-$S$ system

Using a recently proposed measure for divisibility of a dynamical map, we study the non-Markovian character of a quantum evolution of a driven spin-$S$ system weakly coupled to a bosonic bath. The complete tomographic knowledge about the dynamics of the open system is obtained by the time-convolutionless master equation in the secular approximation. The derived equation can be applied to a wide range of spin-boson models with the Hermitian or non-Hermitian coupling operator in the system-environment interaction Hamiltonian. Besides the influence of the environmental spectral densities, the tunneling energy of the system Hamiltonian can affect the measure of quantum non-Markovianity. It is found that the non-Markovian feature of a dynamical map of a high-dimension spin system is noticeable in contrast to that of a low-dimension spin system.