Function Expressions for Rate Coefficients

Before presenting a full kinetic theory description of a reacting fluid, we give a more formal microscopic treatment of reactions via linear response theory. This discussion will serve to make the conditions under which we expect the macroscopic rate law to hold more precise, and will also provide 

The discussion presented below is most conveniently given in terms Fourier-Laplace transforms of the density fields 

In this space, the rate law given in (2.19) takes the form 

We shall examine the conditions necessary to obtain this result from the microscopic theory. 

The microscopic basis of the phenomenological rate law can be investigated by making use of projection operator methods. The time evolution of the microscopic density fields, discussed in Section IV, is given by the Liouville equation 

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