  This is an expository note on large deviations, Hamilton-Jacobi-Bellman (HJB)
equations, and the role of the Freidlin-Wentzell quasipotential in Chemical
Reaction Networks (CRNs). The note was motivated by observations which
identified Lyapunov functions for deterministic descriptions of CRNs by taking
appropriate scaling limits of invariant distributions for the corresponding
stochastic dynamics. We explain how this is a special case of a classical
theory due to Freidlin and Wentzell. We also show that this Lyapunov function
is a solution to the HJB partial differential equation if and only if the
network is "complex-balanced". The target audience are researchers in the CRN
community who are familiar with the Markov process description of CRNs, but do
not have the time to invest in learning the technical machinery of large
deviations. We conclude by exploring some possible relationships with K\"ahler
geometry which suggest an interesting and unexplored research direction.
