On the back cover of Fred's book, the velocities of the particles were reversed (to emulate time reversal) and the molecules all return to the original half, though not to the exact original positions, due to rounding errors in the accuracy of the calculations.
The computer calculations used Newton's laws of classical mechanics, which are known to be time reversible and deterministic. If positions of the maolecules and their velocities could be known to arbitrary accuracy, then the future positions (and the past) can be known perfectly, as PierreSimon de Laplace asserted in the early nineteenth century...
"We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes."
The great question for Wolfram, and for Reif, is this: if the equations of motion for microscopic collisions between gas particles are reversible, why are the macroscopic properties of gases irreversible, for example the entropy can only increase, never decrease, as the second law claims.
In a recent YouTube video, Wolfram described the problem,
And in his recent book (p.219), Wolfram describes Fred's book that started his fiftyyear quest to understand the second law.
What is the backstory of the book cover that launched my long journey with the Second Law? The book was published in 1965, and inside its front flap we find:
The movie strips on the covers illustrate the fundamental ideas of irreversibility and fluctuations by showing the motion of 40 particles inside a twodimensional box. The movie strips were produced by an electronic computer programmed to calculate particle trajectories. (For details, see pp. 7, 24, and 25 inside the book.) The front cover illustrates the irreversible approach to equilibrium starting from the highly nonrandom initial situation where all the particles are located in the left half of the box. The back cover (read in the upward direction from bottom to top) illustrates the irreversible approach to equilibrium if, starting from the initial situation at the top of the front cover, all the particle velocities are reversed (or equivalently, if the direction of time is imagined to be reversed). The backcover and frontcover movie strips together, read consecutively in the downward direction, illustrate a very large fluctuation occurring extremely rarely in equilibrium.
Wolfram designed the covers of his book to match the look of Fred's book, but with the computer calculations likely redone using his Mathematica and Wolfram Language tools, or perhaps the evolving hypergraphs of his cellular automata?
Since Newton's microscopic laws of motion of the gas particles are completely deterministic and time reversible, the great question for the past onehundred and fifty years is how macroscopically, the gas appears to be irreversible.
What can we say about the views of Fred Reif and Stephen Wolfram on the questions of randomness and reversibility? We can actually tell a lot by looking very carefully at the results of their computer calculations shown on the front and back covers of their books.
Here are the two movie strips side by side.
Reif Statistical Physics

Wolfram The Second Law

Let's now carefully compare the starting frame on the front covers to the ending frame on the back covers. What can we say about the physics?
Both back covers start by reversing the velocities of the molecules in the last frame on the front cover. Wolfram shows that by reversing the little white arrows.
Both evolve back to the left half of the frames, as if time itself was being reversed.
But note that Reif's computations do not return each molecule back to its exact starting position, as do Wolfram's (The Wolfram back cover sadly cuts of the bottom row of four molecules.) And Wolfram's molecules are in a rigid grid pattern, perhaps an artifact of his cellular automata?