We investigate the divisibility properties of the tensor products Λ^(1)_t⊗Λ^(2)_t of open quantum dynamics Λ^(1,2)_t with time-dependent generators. These dynamical maps emerge from a compound open system S1 + S2 that interacts with its own environment in such a way that memory effects remain when the environment is traced away. This study is motivated by the following intriguing
effect: one can have Backflow of Information (BFI) from the environment to S1 + S2 without the same phenomenon occurring for either S1 and S2. We shall refer to this effect as the Superactivation of BFI (SBFI).
