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In this work, we analyze the spread and transfer of quantum information in large quantum systems under external control. We focus on the entanglement entropy growth rate as a key quantity, employing tools such as Fourier analysis, Hamiltonian quantization, and out-of-time-ordered correlators (OTOCs). Our goal is to derive a corrected expression that captures the role of external control while ensuring consistency with fundamental physical principles, in particular the constraint that the entanglement entropy cannot exceed the maximal bound \(S_{\max}\) in closed systems.