The equation arises not by analyzing the individual positions and momenta of each particle in the fluid but rather by considering a probability distribution for the position and momentum of a typical particle—that is, the probability that the particle occupies a given very small region of space (mathematically the volume element d 3 r ) centered at the position r , and has momentum nearly equal to a given momentum vector p (thus occupying a very small region of momentum space d 3 p ), at an instant of time.