Abstract
On the basis of a cluster expansion of the classical Liouville operator the Boltzmann equation is generalized to higher densities. This expansion is analogous to the Mayer expansion known in equilibrium statistical mechanics, and furnishes a simple prescription to write down the terms of the higher order in the number density for the spatially homogeneous as well as the spatially inhomogeneous case. As the boundary conditions for the distribution functions the weakening of the correlation of the initial distribution is employed.
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