Modeling the Probabilities in Chemical Reactions

Deflnitions. The basic elements of Markov chains associated with Eq.(2-24) are the system, the state space, the initial state vector and the one-step transition probability matrix. Considering refs.[26-30], each of the elements will be defined in the following with special emphasize to chemical reactions occurring in a batch perfectly-mixed reactor or in a single continuous plug-flow reactor. In the latter case, which may simulated by perfectly-mixed reactors in series, all species reside in the reactor the same time. 

The system is simply a molecule. The state of the system is the specific chemical formula of the molecule, or what kind of species is the molecule. The state space is the set of all states that a molecule can occupy, where a molecule is occupying a state if it is in the state. For example, in the following irreversible consecutive reaction  

The state space SS, which is the set of all states a system can occupy, is designated by  

Finally, the reaction from state Aj to state Aj is the transition between the states. The initial state vector is given by Eq.(2-22), i.e.  

The reacting system. Consider a chemically reacting system containing 

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