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The energy that determines the transport of electrons through a single-electron device
is Helmholtz's free energy which is defined as difference between
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.
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.