Thermodynamics and statistical mechanics hold a bit of an odd place in the heart and mind of a physics student. On one hand it’s one of the few subjects with truly universal applicability. No matter if you work in galaxy clusters, nuclear theory, experimental solid state, or anything else the concepts of those disciplines are going to assert themselves. Energy and entropy are everywhere. On the other hand it tends to be a tremendous pain in the neck to learn.

I’m in a stat mech class this semester, as you might guess. We do about two days worth of thermodynamics to keep up appearances, but by the time you get to the graduate physics level thermo is essentially an engineering problem. Statistical mechanics is the heart of the issue.

Now as today is day 1 and we haven’t yet done all that much, I’m not going to go into any detail here either. I just want to give you a brief taste of the weirdness. Trust me, I’m going to take advantage of this class to write about plenty of weirdness on this site as the semester goes into full swing.

Take pressure, for instance. We know it’s force per unit area. Slightly more esoterically, we’re probably also aware that it’s the derivative of energy with respect to volume. That has more thermodynamic significance, but then perhaps more relevant is this weird creature:

That’s more than a little bizarre, in my opinion. Pressure is equal to the temperature times the derivative of entropy with respect to volume – number of particles and total energy held constant. I wouldn’t find that intuitively obvious at all. Of course it works out dimensionally: the entropy S has units of energy per temperature, so you end up with overall units of energy per volume which matches the more common-sense definition above.

Things get weirder. You can without too much trouble extract a similar-looking equation for volume. Volume is an even more concrete thing to measure than pressure and so to see it written in terms of thermodynamic variable like entropy is a little disconcerting. True nonetheless, however.

And people say quantum mechanics is weird.