# Statistical physics at very large particle number

According to this manuscript

http://www.math.lmu.de/~michel/credits/Federica_Pezzotti_phd.pdf

it is proposed (e.g. at page 18) that particle correlations between particles can be neglected in the super-large particle number Limit $$N \mapsto \infty$$. That means that if the system exhibits a pair potential $$V_{ij}$$ between particle i and particle $$j$$, the kinetic equations of the system will simplify to a Vlasov-like equation. Can additional collision terms (arising from the correlation functions) besides the mean-field potential $$\langle V_{ij} \rangle$$ really be neglected, when statistics of a huge number of particles is considered?

Or in other words: If we want to describe Billard balls made of zillions of Atoms with a 1-particle Distribution $$f(x,v,t)$$ (probability density that any ball will be at $$x$$ with Velocity $$v$$ at time $$t$$), is it enough to consider the equation

$$\partial_tf+\partial_x(vf)-\frac{1}{m}\partial_v(\nabla \langle V_{ij} \rangle f)=0$$

$$\langle V_{ij} \rangle (x) := \int d^3w \int d^3y f(y,w,t) V_{ij}(y-x)$$

without an extra collision term on the right hand side?