2.3 Helmholtz's Free Energy

     The energy that determines the transport of electrons through a single-electron device is Helmholtz's free energy which is defined as difference between total energy $E_{\Sigma}$ stored in the device and work done by power sources. The total energy stored includes all the before mentioned energy components that have to be considered when charging an island with an electron.
 $$\begin{gather} F = E_{\Sigma} - W \qquad\text{with}\qquad E_{\Sigma}=E_C+\Delta E_F+E_N. \end{gather}$$
The change in Helmholtz's free energy a tunnel event causes is a measure of the probability of this tunnel event. The general fact that physical systems tend to occupy lower energy states, is apparent in electrons favoring those tunnel events which reduce the free energy.