Sketch of the region at one location in the six-D phase space, with directions in x and Vx shown. The rate of change of particles within the rectangle is equal to the difference between the flows in and the flows out. This equality leads directly to the collisionless Boltzmann equation (CBE). The relevance of "collisionless" is that a collision causes an instantaneous change in velocity (not position) so particles can disappear from a location in the phase space and reappear elsewhere -- hence the equality doesn't hold.