[1] Jerry Pournelle should know better.

He writes once again of his confusion about how the universe used to be in a state of lower entropy but now is in a state of higher entropy, yet one in which Shakespeare, Beethoven, and Sagan trod the Earth.

The narrow technical question is easy to answer. Free expansion increases entropy. That this is true for an ideal gas is an exercise that any undergraduate engineer or physics student can demonstrate. In fact, the increase in specific entropy for a fixed mass of ideal gas is the gas constant times the natural log of the volume ratio:

[2]

since the temperature of the gas is constant for a free expansion. The more general case of a relativistic fluid requires more sophisticated mathematical machinery, but the principle is the same.

I also feel obligated to dispense with a common fallacy: “The Second Law of Thermodynamics only applies to closed systems.” Again, any undergraduate engineer should have been forced at gradepoint to learn the “flow” version of the second law:

[3]

In plain English, the amount of entropy inside a control volume can increase or decrease, depending on mass flows and heat flows into and out of the control volume,  but — since the entropy transfer through the control surface is conservative — the total amount of entropy in the universe can only increase and never decrease. This observation does not depend on the system being closed.

The not-so-narrow technical question is related to [4] what Sean Carroll was commenting on. I would say the interesting question is: “Why does the ’state vector’ of the universe wander into regions of larger entropy?” Actually, though, [5] Sean seems to be asking a slightly different question, which is why the universe wasn’t created in a state of really really high entropy — and what if there are alternative ways for the universe to be? Frankly I’m skeptical of the utility of this line of thinking, but I have to admit one line in Sean’s SciAm essay caught my imagination: “Whereas we can relate the entropy of a fluid to the behavior of the molecules that constitute it, we do not know what constitutes space, so we do not know what gravitational microstates correspond to any particular macrostate.” I have no idea what he’s talking about, but it sounds like there might be a there there, as it were. Is there a statistical mechanics of quantum gravity? I suppose we’ll only know once we have the quantum gravity part worked out. In the meantime, I suspect that speculations about universes in which omelots unmake themselves are sterile.

My own personal preference for a grand cosmological theory is Andrei Linde’s “[6] self-reproducing inflationary universe“. In this view, the Big Bang was one little knot in a much larger tapestry, a not-so-singular event that only seems unphysical in the absence of a clear understanding of inflation. This approach seems to resolve some problems of long standing, in particular addressing the puzzles of the singularity and the apparent lack of prior cause. On the other hand, like many cosmological speculations, it borders on unverifiability, and thus risks losing its status as a scientific hypothesis.

Full disclosure: Sean Carroll and I were at the [7] CTP at the same time; we knew each other tangentially, though he was several years ahead of me in grad school. I always enjoyed his lectures.

UPDATE: Jerry says I have misunderstood his concern. He writes: “My only point was that the explanation of Time’s Arrow was more glib than persuasive.” Fair enough. I have always been suspicious of the implication that the direction of entropy increase has anything more than the obvious connection to the direction of time.