The collision term in the Boltzmann equation can be derived from the BBGKY hierarchy.
In statistical physics, the BBGKY 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.
Does this mean, if I have a system consisting of s particles, that there is an interaction with a particle outside my system? So my system is not closed?