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.

翻译：尽管隔室动力学系统在科学的许多不同领域中得到广泛应用，但由于缺乏量化这类系统熵的方法，基于最大熵原理（MaxEnt）的模型选择仍具挑战性。在此，我们利用隔室系统作为连续时间马尔可夫链的解释，获取量化模型信息含量的熵测度。具体而言，我们通过路径熵和熵率量化单个粒子在系统中移动路径的不确定性。路径熵衡量粒子从进入系统到离开的完整路径的不确定性，而熵率则衡量粒子在系统期间其瞬时未来的平均不确定性。基于香农信息熵，我们推导了平衡态下隔室系统这两种熵的显式公式，并展示了它们如何通过MaxEnt解决模型选择过程中的等终态问题。