Assumption of molecular chaos Assumption of molecular chaos in statistical mechanics states that the incoming velocities of two colliding particles are uncorrelated. 
Now, since it introduces a direction of time, this hypothesis obviously could not be derived from the classical equations of motion for particles (F=ma and etc., or their more mathematically elaborated counterparts). 
My question is: are there any logical arguments showing the above hypothesis is compatible with (i.e. does not imply something strongly contradicting) the Newtonian equations of motion, other than that it manages to provide predictions agreeing with experiments?
My own thoughts on this: since it breaks the time-reversal symmetry of the classical model, molecular chaos is indeed incompatible with the classical equations of motion. But this raises the further question of why, then, are we allowed to use classical mechanics everywhere else in statistical mechanics.
 A: For systems of point particles, equations of motion in non-relativistic mechanics are such that initial condition is positions and their first derivatives, but not higher derivatives of position.
But as far as values of those positions and velocities go, one can choose any, equations of motion do not limit them in any way. Thus special condition such as the decorrelation hypothesis are fine in  mechanics. 
A: First note that it is an assumption of molecular chaos. You can see it as a prerequisite to apply statistical mechanics. Does the assumption fail? No statistical mechanics for you!
So does it introduce a direction of time? I think not because whether the particles are correlated or not depends on your initial conditions. You put uncorrelated velocities in and you get uncorrelated velocities out. In equilibrium the system is time reversible because then the entropy doesn't increase and $\text dS=0$. The process of correlated velocities becoming uncorrelated breaks time symmetry sure. But once you have an equilibrium state the system is time symmetric.
