 Molecular chaos for the Boltzmann equation

The incoming two-particle distribution at a collision is approximated by the product of one-particle distributions. This closes the binary collision term into the quadratic nonlinear Boltzmann collision operator. It does not assert exact independence after collisions: outgoing pairs can be correlated, and time reversal generally converts those correlations into incoming correlations. A rigorous kinetic limit needs propagation and convergence estimates rather than a bare independence assertion.