 The definition of capacitance,

with the potential difference

may be applied to the device with the addition or removal of individual electrons,

Then

is the "quantum capacitance" of the device.This expression of "quantum capacitance" may be written as

which differs from the conventional expression described in the introduction where formula_28, the stored electrostatic potential energy,

by a factor of 1/2 with formula_30.However, within the framework of purely classical electrostatic interactions, the appearance of the factor of 1/2 is the result of integration in the conventional formulation,

which is appropriate since formula_32 for systems involving either many electrons or metallic electrodes, but in few-electron systems, formula_33.