BBGKY hierarchy

In statistical physics, the BBGKY hierarchy (Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy, sometimes called Bogoliubov hierarchy) is a set of equations describing the dynamics of a system of a large number of interacting particles. The equation for an s-particle distribution function (probability density function) in the BBGKY hierarchy includes the (s + 1)-particle distribution function thus forming a coupled chain of equations. This formal theoretic result is named after Bogoliubov, Born, Green, Kirkwood, and Yvon.

The evolution of an N-particle system in absence of quantum fluctuations is given by the Liouville equation for the probability density function ${\displaystyle f_{N}=f_{N}(\mathbf {q} _{1}\dots \mathbf {q} _{N},\mathbf {p} _{1}\dots \mathbf {p} _{N},t)}$ in 6N dimensional phase space (3 space and 3 momentum coordinates per particle)

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