Irreversible A B — C reaction. Fluctuations of the concentration difference

Let us consider now the irreversible A - - B — C reaction in the case of equal reactant concentrations, ua = ub, following Ovchinnikov and Zeldovich [35]. The reaction kinetics obeys the equations 

Due to inevitable fluctuations - both thermodynamical or related to the system s prehistory, quantities CA r,t) and C B(r, f) are not identical but their volume averages coincide  

In other words, the kinetics of smoothing out of Z f,t) fluctuations is governed by a simple linear diffusion equation which solution and, in particular, the Green function, are well known. Similarly to (2.1.43), (2.1.45) we can now write down 

Let us consider now the extreme case of an instant reaction, /c — oo. In this case particles A and B do not coexist in physically infinitesimal volumes. The solution of (2.1.68) comes from putting there the cofactor of k to zero, i.e.. 

In other words, the reaction kinetics at A oo is entirely determined by dijfusive encounter of reactants since in the degenerate problem, described by (2.1.65) and (2.1.69), a role of diffusion is self-evident. Equation (2.1.69) means that whole volume is indeed divided into blocks characterized by a sign of Z f,t) for Z r,t) 0, C r,t) = Z f,t), CB r,t) = 0 and vice versa. 

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