BBGKY hierarchy

Summary

The BBGKY hierarchy is a system of equations for the reduced distribution functions of a system of $N$ interacting classical particles. The equation for the distribution of $s$ particles involves the distribution of $s + 1$ particles, so the system forms a chain of $N$ coupled equations. It is exactly equivalent to the Liouville equation for the full $N$-particle density. Closing the chain by an approximation leads to the kinetic equations, such as the Boltzmann equation and the Vlasov equation. The name comes from Bogoliubov, Born, Green, Kirkwood and Yvon.