  Reaction networks are a general formalism for describing collections of
classical entities interacting in a random way. While reaction networks are
mainly studied by chemists, they are equivalent to Petri nets, which are used
for similar purposes in computer science and biology. As noted by Doi and
others, techniques from quantum field theory can be adapted to apply to such
systems. Here we use these techniques to study how the "master equation"
describing stochastic time evolution for a reaction network is related to the
"rate equation" describing the deterministic evolution of the expected number
of particles of each species in the large-number limit. We show that the
relation is especially strong when a solution of master equation is a "coherent
state", meaning that the numbers of entities of each kind are described by
independent Poisson distributions.
