A key insight applied by Boltzmann was to determine the collision term resulting solely from two-body collisions between particles that are assumed to be uncorrelated prior to the collision. This assumption was referred to by Boltzmann as the "" and is also known as the "molecular chaos assumption". Under this assumption the collision term can be written as a momentum-space integral over the product of one-particle distribution functions:
where  and  are the momenta of any two particles (labeled as A and B for convenience) before a collision,  and  are the momenta after the collision,
is the magnitude of the relative momenta (see relative velocity for more on this concept), and  is the differential cross section of the collision, in which the relative momenta of the colliding particles turns through an angle  into the element of the solid angle , due to the collision.