Callen H.B - Thermodynamics And An Introduction To Thermostatistics · Problem 11.1-1

The Nernst postulate states that entropy approaches zero as temperature approaches absolute zero. For a two-level system, you need to calculate the entropy using the statistical mechanics definition—counting how many microstates are accessible at a given $T$—and then examine its behavior as $T \to 0$. The key insight is that even at very low temperatures, both energy levels remain slightly populated due to thermal excitation, so the system never becomes completely ordered into a single state. Check whether $S(T) \to 0$ or remains finite as $T \to 0$ to determine if the postulate holds.

The Nernst postulate states that entropy approaches zero as temperature approaches absolute zero. For a two-level system, you need to calculate the entropy using the statistical mechanics definition—counting how many microstates are accessible at a given $T$—and then examine its behavior as $T \to 0$. The key insight is that even at very low temperatures, both energy levels remain slightly populated due to thermal excitation, so the system never becomes completely ordered into a single state. Check whether $S(T) \to 0$ or remains finite as $T \to 0$ to determine if the postulate holds.