The Second Law of Thermodynamics probably produces more confusion in the general public than most other physical laws that have percolated themselves into the collective consciousness. Not the least of these are all the seemingly disconnected ways of saying it, which vary in accuracy. Disorder increases. Absolute zero is impossible. Engines can’t turn heat into work with perfect efficiency. Things fall apart, the center cannot hold, mere anarchy is loosed upon the world…

Well maybe not that last one.

Probably the version that both makes the most sense and is the most accurate is one that’s rarely stated outside of physics books. Before I state it, I want to build up an example to illustrate the point. Consider the flipping of four fair coins. You take them out of your pocket and fling them into the air. You can take my word for it that there are sixteen ways that they can land, and here they all are:

HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT.

All of them are equally probable, with a 1 in 16 chance each. On the other hand, we’re not keeping track of which coin does which. We’re only interested in how many heads and how many tails there are. And not all of those are equally probable. For instance, there’s one way each to get all heads or all tails. Both of those are a 1 in 16 chance. But to get two heads and two tails there’s six possibilities, making the chance of that 3 in 8 – considerably more likely. That is the heart of the second law:

A system in equilibrium will probably be in the state with the most ways to create that state.

It’s still a little informal, but it gets the point across. It may also be objected that physical laws ought not have words like “probably” in them. Fair enough. I wouldn’t worry about it much though. Entropy is mainly useful in describing large collections of particles such as for instance the molecules in a roomful of air. The number of ways to more-or-less evenly scatter the molecules about the room is *unbelievably colossally enormously* larger than the number of ways that they might be all put to one side of the room. And so you’re not going to suddenly find yourself in a room where all the molecules just happen to all be somewhere else. My very rough back-of-the-envelope suggests that for even a quite small volume of gas (say, one mole’s worth) the imbalance between two halves of a room will essentially never be above one part per trillion.

Even this tiny “violation” of the second law is perfectly kosher though, because the law is formally a statistical statement. The details of those statistics get hairy, but the gist of the very interesting but headache-inducing statistical mechanics class I’m taking this semester is just the words in the blockquote.