On the General Theory of the Approach to Equilibrium. III. Inhomogeneous Systems

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Abstract
We find the evolution equation for a singlet distribution function in a fluid containing macroscopic inhomogeneities. The equation, a generalization of the Boltzmann equation, derived from the Liouville equation, may be written formally to any order in either concentration or strength of interaction. We find f1 to be a functional only of itself and other f1's. We then show that initially present correlations are destroyed during the same relaxation time as in homogeneous systems. We can then write formally to any order the equation for a reduced s‐particle distribution function fs, which proves to be a functional of a product of f1's, all the time dependence of the fs being lodged in the f1's for times greater than the relaxation time.