$T \to 0$ ($x \to \infty$): $p_0 \to 1$, $p_1 \to 0$. $S \to 0$. The system freezes into the ground state (pure). - $T \to \infty$ ($x \to 0$): $p_0, p_1 \to 1/2$. $S \to \ln 2$. The system is maximally mixed.