We investigate the dynamics of entropic uncertainty relations, tightness, and concurrence in two non-interacting qubits produced in the Werner state and subjected to classical channels. In two contexts, common and independent qubit-noise configurations, a Gaussian Ornstein Uhlenbeck process is used to control the noisy effects of the local external fields. Using parameter optimization, we establish long-term stability in two qubits while reducing the environment's disorder entropic impact and maintaining entanglement. Using entropic uncertainty relations, tightness and concurrence, we show that in the presence of Ornstein Uhlenbeck noise, two-qubit coherence and entanglement in local fields are both weak and readily lost. Despite this, longer entanglement and lower entropy can be predicted within a limited range of the noise parameter and purity estimator of the two-qubit state. Furthermore, the measured rate of entropy rise outpaces the rate of disentanglement generation. In addition, we also utilized the tightness measure to estimate the uncertainty in the dynamics of bipartite entropic relations.

The behavior of the uncertainty relations and their tightness for a system, consisting of two qubits interacting thermally with a magnetic field in the presence of Dzyaloshinskii–Moriya interaction, is discussed, where different types of interaction strengths are considered. It is shown that both coupling and the magnetic field parameters decay the degree of entanglement, and increasing the uncertainty relations and the degree of mixedness. The phenomena of the sudden changes in the investigated quantities are depicted at large values of the field and coupling parameters. Concerning the type of the coupling parameters, distance and the trigonometric coupling have a clear effect on the behavior of the studied physical quantities.

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