  Systems of coupled rate equations are ubiquitous in many areas of science,
for example in the description of electronic transport through quantum dots and
molecules. They can be understood as a continuity equation expressing the
conservation of probability. It is shown that this conservation law can be
implemented by constructing a gauge theory akin to classical electrodynamics on
the network of possible states described by the rate equations. The properties
of this gauge theory are analyzed. It turns out that the network is maximally
connected with respect to the electromagnetic fields even if the allowed
transitions form a sparse network. It is found that the numbers of degrees of
freedom of the electric and magnetic fields are equal. The results shed light
on the structure of classical abelian gauge theory beyond the particular
motivation in terms of rate equations.
