  Although compartmental dynamical systems are used in many different areas of
science, model selection based on the maximum entropy principle (MaxEnt) is
challenging because of the lack of methods for quantifying the entropy for this
type of systems. Here, we take advantage of the interpretation of compartmental
systems as continuous-time Markov chains to obtain entropy measures that
quantify model information content. In particular, we quantify the uncertainty
of a single particle's path as it travels through the system as described by
path entropy and entropy rates. Path entropy measures the uncertainty of the
entire path of a traveling particle from its entry into the system until its
exit, whereas entropy rates measure the average uncertainty of the
instantaneous future of a particle while it is in the system. We derive
explicit formulas for these two types of entropy for compartmental systems in
equilibrium based on Shannon information entropy and show how they can be used
to solve equifinality problems in the process of model selection by means of
MaxEnt.
