The Bekenstein bound for systems falling into black holes

Consider a system of energy $E$ and size $R$ falling into a black hole, and let $\Delta S_{BH}$ be the resulting change in black-hole entropy. Bekenstein bound conjecture. The second law of black-hole thermodynamics requires

$$\Delta S_{BH}\geq\frac{2\pi ER}{\hbar c}.$$

The proposed inequality is intended to ensure that the generalized second law is not violated. The source gives no further resolution status.