Effect of Initial Correlation on the Kinetic Equation

In the bulk limit (particle number $N\to \infty$, volume $\Omega \to \infty$ with $\frac{N}{\Omega }≔\mathrm{const}$), the one-body density operator $n\left(t\right)\mathrm{}$ describing interacting distinguishable particles satisfied a closed evolution equation. This equation contains a set of terms which explicitly depend on the initial -correlation operators $\chi$, in contrast with a typical kinetic equation such as Boltzmann's equation. The nature of these terms is investigated. It is explicitly shown that the initial pair correlation ceases to influence the evolution of $n\left(t\right)\mathrm{}$ after a time of the order of a collision duration for a weakly coupled low-density gas.