A truncation scheme for the BBGKY2 equation

Abstract

In recent years, the maximum entropy principle has been applied to a wide range of different fields, often successfully. While these works are usually focussed on cross-disciplinary applications, the point of this letter is instead to reconsider a fundamental point of kinetic theory. Namely, we shall re-examine the Stosszahlansatz leading to the irreversible Boltzmann equation at the light of the MaxEnt principle. We assert that this way of thinking allows to move one step further than the factorization hypothesis and provides a coherent-though implicit-closure scheme for the two-particle distribution function. Such higher-order dependences are believed to open the way to a deeper understanding of fluctuating phenomena.