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The collision term in the Boltzmann equation can be derived from the BBGKY hierarchy.

Wikipedia says:

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?

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No, this is talking about correlations between s random particles. The s-particle distribution function is a 2*d*s (so 6s in 3 dimensional space) dimensional PDF that statistically describes s particles. For s=1, this is just the normal density in phase space. For s=2, this might show, for example, that more often than not two particles are traveling away from each other (maybe they just collided). A good source for this is Ch. 2 in "The Statistical Physics of Particles" by Mehran Kardar.

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