Symmetry-enhanced generation of classical entanglement in driven Brownian systems

We analytically investigate the generation of entanglement in a system of two coupled Brownian particles subjected to time-dependent, dual-driving protocols. By modeling the system as a bivariate Ornstein-Uhlenbeck process, we derive the dynamics of the entanglement witness, W(t), from the deterministic Lyapunov equation governing the covariance matrix. We compare symmetric and asymmetric driving protocols and show that symmetric driving is fundamentally more efficient at generating entanglement. This advantage is traced to the preservation of variance symmetry, which optimizes the witness function. Furthermore, we develop a predictive model for the optimal interaction strength, g_{opt}, using a time-averaged effective potential. This model demonstrates that optimal coupling is protocol dependent, providing a clear framework for controlling emergent correlations in driven mesoscopic systems.