  The Landau-Lifshitz-Gilbert (LLG) and Landau-Lifshitz (LL) equations play an
essential role for describing the dynamics of magnetization in solids. While a
quantum analog of the LL dynamics has been proposed in [Phys. Rev. Lett. 110,
147201 (2013)], the corresponding quantum version of LLG remains unknown. Here,
we propose such a quantum LLG equation that inherently conserves purity of the
quantum state. We examine the quantum LLG dynamics of a dimer consisting of two
interacting spin-1/2 particles. Our analysis reveals that, in the case of
ferromagnetic coupling, the evolution of initially uncorrelated spins mirrors
the classical LLG dynamics. However, in the antiferromagnetic scenario, we
observe pronounced deviations from classical behavior, underscoring the unique
dynamics of becoming a spinless state, which is non-locally correlated.
Moreover, when considering spins that are initially correlated, our study
uncovers an unusual form of transient quantum correlation dynamics, which
differ significantly from what is typically seen in open quantum systems.
