The collisio operator and long-time behavior of a perturbed two-body problem

The nature of the collision operator for a classical mechanical system whose dynamics is represented by a probability density satisfying the Liouville equation is illustrated with a soluble example. This example is that of a two-body problem with a particular perturbation. The collision operator is found and the time reversibility of the system is examined utilizing the analysis of Stey. For negative energies, the collision operator is zero in the limitzi0⁺, while for zero energy, the collision operator is different from zero in that limit. This indicates that the system is reversible for negative energy and irreversible for zero energy.