That is: One instructor's humble attempt to both formulate and answer the former's reversibility objection to the latter's statistical-mechanical explanation of the second law of thermodynamics (in a Newtonian context)
Please contact me if you can confirm or refute either my formulation of the objection or my answer to it!
The reversibility objection: Let us suppose that an isolated volume of gas is evolving toward greater entropy. If the velocities of all the particles in this gas were reversed, it would evolve toward lower entropy. Furthermore, Boltzmann's assumptions seem to imply that it is equally probable for the particles in the gas to have the positions and velocities involved in the second, entropy-decreasing scenario as in the first, entropy-increasing scenario. Doesn't this mean that entropy is just as likely to decrease as to increase?
An answer: No. For the sake of illustration, let us represent as real numbers between 0 and 99 all sets of exact molecular positions and velocities that entail increasing entropy of the gas as a whole. For any such scenario represented by a given real number x, assign the corresponding scenario with velocities reversed the number 99 + (x/99). Finally, suppose that probability is uniformly distributed across the interval from 0 to 100. For every entropy-increasing scenario, then, there is then an equally probable entropy-decreasing scenario. (Strictly speaking, the two scenarios have equal probability density.) But overall, it is still 99 times more probable that the gas is increasing than that it is decreasing in entropy.