Behavior of stochastic reaction network towards the thermodynamic limit

An important concept for describing chemical reaction networks is the thermodynamic limit, where the number of molecules and the size of the system are asymptotically large. Systems in the thermodynamic (macroscopic) limit can be modeled with a deterministic modeling formalism; away from it, at the microscopic limit, a stochastic approach is more suitable . However, due to numerical and computational difficulties, little is known for the behavior of networks in the mesoscopic area, where the system is sizable yet still under the influence of thermal noise.
We employ the Schlögl model reaction network, a simple single component system, to provide useful information about the mesoscopic behavior of chemical reaction networks. For our analysis ZI-closure scheme method is used. This is a numerical solution of chemical master equations, which utilizes the maximization of the system entropy. To our knowledge this is the first time such an analysis is presented for the transition between stochastic and deterministic chemical reaction models with computational tools.