Adiabatic scaling of a Fermi gas with power-law density of states
= Adiabatic scaling of a Fermi gas with power-law density of states
For <density of states> $AV\epsilon^a$, $a>-1$, the <grand canonical ensemble> has $\log\mathcal Z=VT^{a+1}f(\mu/T)$. <Strict monotonicity of Fermi gas entropy per particle> makes $\mu/T$ constant at fixed entropy and particle number. Therefore $VT^{a+1}$ and $PV^{(a+2)/(a+1)}$ are constant along a reversible <adiabatic process>.