I've been deepening my understanding of the 2nd Law, mostly through failed attempts to subvert it, which is a disreputable enterprise but one full of interest if approached in the right spirit.
I now think I understand the notion of thermal equilibrium much more deeply than before. I think the way we teach thermodynamics is all wrong--we ought to teach statistical stuff first, and only then look at the classical concepts. This makes sense:
- Heat is the internal energy of molecular motion
- Entropy is a measure of the number of different ways the molecules can be re-arranged but still have the same energy
- Temperature is the inverse of the derivative of change of the number of ways the molecules can be rearranged with the change in heat energy.
Thermodynamics often gets taught in such a way that entropy seems strange--I remember one of my professors saying something like, "Entropy hardly seems like a human concept at all" and going on to praise Joule and Kelvin and others for their genius in arriving at it. In retrospect, entropy looks perfectly sensible. Temperature looks weird.
In particular, temperature seems to require a counter-factual to define it generally: it is the inverse of the rate of change of entropy with heat if we were to change the amount of heat in a body. But what if we don't? Is the temperature of an isolated body something that exists only in potentia?
There's something strange going on here, and I don't understand yet what it is. My real interest is in understanding thermal equilibrium, but to do that I need to understand temperature, and I don't.