= Thermal pair creation heat capacity for touching parabolic bands
{title2=$N_c=Dk_BT\ln2,\quad C/N_c=\pi^2k_B/(3\ln2)$}
For symmetric touching <parabolic dispersions> with constant <density of states> $D$ per <energy band>, including <spin degeneracy>, <charge neutrality> fixes $\mu=0$. The <Fermi-Dirac distribution> gives $N_c=Dk_BT\ln2$ and the thermal <internal energy>, including <electrons> and <holes>, is $\Delta U=(\pi^2/6)D(k_BT)^2$. Thus $C=(\pi^2/3)Dk_B^2T$. Its large ratio to $N_c$ is compatible with the <equipartition theorem> because this excitation count grows with <temperature> and the <heat capacity> includes both species.
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