Nonlinear quantum multi-spin dynamics without entanglement

We introduce a distinct route for extending classical atomistic spin dynamics into the quantum regime for arbitrary spin s, based on a variational product-state ansatz that includes both pure and mixed local states. By construction, intersite entanglement -- expected to remain negligible even on very short time scales in many real materials -- is excluded, while local quantum effects are retained through the nonclassical structure of s at least 1 density operators, and nonlinear dynamics arise from both the mean-field interdependence of the local states and the state-dependent dissipative terms. This framework clarifies the variational and geometric origin of the inequivalence between quantum Landau-Lifshitz and Landau-Lifshitz-Gilbert dynamics, provides a criterion for their equivalence under a common time rescaling, establishes connections with the classical theory through two qualitatively distinct limits (s to infinity and a large number of quantum spins N), and allows realistic O(N) simulations of quantum spin dynamics in materials.