Disorder through Order

My latest story went up at Physical Review Focus on Friday. The most obvious hook to this story is that a highly simplified system has more entropy if it forms a crystal than as a random, liquid-like arrangement. This is surprising because randomness usually means higher entropy.

As often happens when looking deeper into a single journal article, though, this finding really isn't all that new. In fact, the first simulations of this effect, for collections of spheres (known as "hard spheres" by the cognoscenti), were done some 50 years ago. A decade or so ago, theoretical and experimental research confirmed that the higher entropy arises because all of the atoms in the crystal have some room to rattle around. Other things being equal, entropy is higher if any extra wiggle room is distributed democratically among all degrees of freedom. (We're not talking about a close-packed crystal here, where all of the spheres are butted together like cannonballs or oranges, but one where they jiggle around in a looser arrangement, each one on average in a crystalline position.) In contrast, a random arrangement of spheres with the same density as this loose crystal becomes "jammed" into a rigid network, with only a few "rattlers" free to move.

Moreover, it's extraordinarily common for order to develop in complex systems, in spite of the apparently irresistible demand of the Second Law of Thermodynamics that entropy never decrease. The catch is that the total entropy increases by slightly increasing the jiggling of a large number of degrees of freedom to pay for a large-scale ordering. Such spontaneous pattern generation occurs everywhere from chemical reactions to thermal convection to--most important for us--life itself.

The thing that actually made this story new was that the spheres were connected together to form a kind of idealized polymer, but could otherwise move freely. The polymer molecules themselves don't arrange regularly, but the spheres do. In some ways the simulation stacked the deck in favor of the crystallization by making them as similar to the bare spheres as possible, but it's a kind of existence proof that even the polymer can crystallize due to entropy alone. Connecting the spheres in a polymer didn't stop it.

The journalistic challenge is to convey the exciting, surprising part without leaving a misleading idea about what was new. Sometimes this can be quite hard or even impossible, if the advance involves a highly technical issue. In this case, the basic ingredients were not that hard to get across (other than entropy itself), so it wasn't too hard to get both the history and the novelty into a short format. The alternative is to neglect the history and let readers think that this new article has created a completely new understanding. Unfortunately, news stories are told this way much more often than they should be.