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We will show how to generate entangled states out of unentangled states on a bipartite system by means of dynamical boundary conditions. The auxiliary system is defined by a symmetric but not self-adjoint Hamiltonian, and we will also study the space of self-adjoint extensions of the bipartite system. We will show that only a small set of these extensions leads to separable dynamics, and we will characterize these extensions. Various simple examples illustrating this phenomenon are discussed; in particular, we will analyze the hybrid system consisting of a planar quantum rotor and a spin system under a wide class of boundary conditions.