The entropy–mass bound for black holes

Let $S=A/(4G\hbar)$ be the Bekenstein–Hawking entropy of a black hole with mass $M$ and horizon area $A$. Entropy–mass bound conjecture. The entropy should satisfy

$$S\leq\frac{4\pi M^2}{\hbar},$$

with equality for Schwarzschild black holes. Equivalently, $A\leq16\pi M^2$. The source presents this as the Penrose inequality in thermodynamic form and gives no separate resolution status.