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The quantum capacitance per unit area is $c_q=e^{2}D(E_F)$. Differentiating the gate equation givesThus the available electronic states act as a second contribution in series with geometric capacitance. At exact neutrality the ideal zero-temperature model has $c_q=c_{\mathrm{diff}}=0$; actual finite-temperature or spatially nonuniform samples need a broader description. A capacitance measurement can therefore probe the density of states, rather than geometry alone.