Analyzing the Spread and Transformation of Quantum Information in Large Quantum Systems Under External Control

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.