= Equal-degeneracy two-level energy and heat capacity
{title2=$C=Nk_Bx^2e^x/(1+e^x)^2$}
For N <independent> units with nondegenerate levels 0 and $\Delta>0$, the <canonical partition function> is $(1+e^{-\beta\Delta})^N$. Its <energy> is $N\Delta/(1+e^{\beta\Delta})$ and <heat capacity> is $Nk_Bx^2e^x/(1+e^x)^2$, with $x=\Delta/(k_BT)$. Both are activated at low <temperature>. At high <temperature> the <energy> saturates at $N\Delta/2$ and <heat capacity> decays as $T^{-2}$. The equal-degeneracy Schottky peak is at $x\simeq2.39936$ and height $0.43923Nk_B$. A common <energy> shift leaves <heat capacity> unchanged; unequal level degeneracies require a different <partition function>.
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