We formulate a linear theory of physical kinetics describing the relax
ation of atoms from a non-equilibrium distribution. The evolution of t
he single-particle distribution function is decomposed into trajectori
es, each corresponding to a different realization of a sequence of col
lisions. Accumulating all possible trajectories gives the dynamics des
cribed by the classical Boltzmann equation. The significance of our me
thod is that the required computation time scales linearly with the nu
mber of points used to sample the distribution function. This leads to
the interesting possibility of extending our method to consider quant
um coherences and the growth of long-range order in Bose-Einstein cond
ensation where a large set of basis states may be required.