"The mechanics underlying Boltzmann's H-theorem are time-symmetric in themselves, however. How then does he manage to derive a time-asymmetric conclusion, namely that H decreases over time? Not surprisingly, the answer is that he has actually imported a time-asymmetric assumption. It is the Stosszahlansatz, or "assumption of molecular chaos". In effect, this is Maxwell's assumption that the probabilities (or, more strictly, frequencies) of velocities of colliding particles are independent."

Why is this an asymmetric assumption? because we expect the velocities of particles to become correlated as a result of their collisions. We expect outgoing products of collisions to be correlated with one another in various ways, even if they never encounter one another in the future. We do not expect the incoming components of a collision to be correlated, if they have never encountered one another in the past."