According to this manuscript


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?


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