 The capacitance of a connected, or "closed", single-electron device is twice the capacitance of an unconnected, or "open", single-electron device.This fact may be traced more fundamentally to the energy stored in the single-electron device whose "direct polarization" interaction energy may be equally divided into the interaction of the electron with the polarized charge on the device itself due to the presence of the electron and the amount of potential energy required to form the polarized charge on the device (the interaction of charges in the device's dielectric material with the potential due to the electron).The derivation of a "quantum capacitance" of a few-electron device involves the thermodynamic chemical potential of an "N"-particle system given by

whose energy terms may be obtained as solutions of the Schrödinger equation.