Abstract
We develop here a theory of molecular fluctuations caused by chemical reactions which keeps track of the chemical identity of individual molecules. The theory is Markovian and can be used to derive birth and death equations for number fluctuations which are identical to the customary coarse-grained chemical “master equation”. We also derive the hierarchy of equations which govern the correlations among groups of particles. These equations uncouple only in the case of strictly unimolecular reactions. For bimolecular reactions we prove a version of Kac's factorization theorem and use it to solve the hierarchy in the thermodynamic limit. Finally, we discuss the relationship of the birth and death theory to our fine-grained theory and examine their mutual limitations.
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