Again entering the realm of interesting physics from last month: a group of scientists proposed a new and quite promising explanation for the Mpemba effect, the observation that warmer water sometimes freezes faster than colder water.

The Definition

Oddly enough, even though the Mpemba effect has been known since ancient times, and its namesake paper was published over half a century ago, physicists can’t even seem to agree on a precise definition of the effect. What we know is that, if you take two containers of water (or, evidently, a water-based mixture like milk) which are identical in every respect except that one is at a higher temperature than the other, and you put them both in a freezer, under some conditions the one at the higher temperature will freeze before the one at the lower temperature. But what conditions are those? And what exactly does it mean to freeze first? Freezing is an extended process, after all; is it talking about when the water reaches zero degrees (Celsius), or when it begins to form ice, or when it is completely converted into ice, or something else?

Part of the contribution of this new paper is a proposal of …

I’m a sucker for good (or bad) physics puns. And the latest viral physics paper (arXiv preprint) allows endless opportunities for them. It’s actually about a system with a negative temperature!

Negative temperature sounds pretty cool, but I have to admit, at first I didn’t think this was that big of a deal to anyone except condensed matter physicists. Sure, it could pave the way for some neat technological applications, but that’s far in the future. The idea of negative temperature itself is old news among physicists; in fact, this isn’t even the first time negative temperatures have been produced in a lab. But maybe you’re not a physicist. Maybe you’ve never heard about negative temperature. Well, you’re in luck, because in this post I’m going to explain what negative temperature means and why this experiment is actually such a hot topic. ⌐■_■

On Temperature

To understand negative temperature, we have to go all the way back to the basics. What is temperature, anyway? Even if you’re not entirely sure of the technical definition, you certainly know it by its feel. Temperature is what distinguishes a day you can walk …

One of the most important principles of thermodynamics is the equipartition theorem:

A system in thermodynamic equilibrium will have an internal thermal energy of \(\frac{1}{2}k_BT\) in each degree of freedom.

But there’s a subtlety here: what exactly are degrees of freedom? There are (at least) two slightly different kinds:

• A mechanical degree of freedom is any way in which a system can freely change its spatial configuration
• A thermodynamic degree of freedom is any way in which a system can freely increase its stored energy

The degrees of freedom the equipartition theorem mentions are the thermodynamic variety. It’s important to know this because the equipartition theorem predicts the heat capacity for many substances in the high-temperature limit, and if if you count the wrong kind of degrees of freedom, you’ll get the wrong answer.

Diatomic molecules

One simple example of this is a diatomic molecule. If you want to figure out how many mechanical degrees of freedom this molecule has, you just count up all the various distances that you need to completely specify the molecule’s spatial configuration. They break down like this:

• Three positions \(x\), \(y\), \(z\) to specify the center of …