Thermodynamics: an antidote to reductionism

In a couple of weeks, I will take over the teaching of a course on “Thermodynamics and Condensed Matter Physics”.  The approach we adopt is one of strictly classical thermodynamics (i.e. no atoms please).  For one thing, this counterbalances the reductionist tendencies implicit in just about all other physics courses that students take.  In this regard, teaching it has also been good for me, since most of my research is focused on simulations done ‘at the quantum level’ (and I don’t think I really appreciated thermodynamics myself as an undergraduate).

Another excellent thing about classical thermodynamics is that it encourages healthy reasoning and problem-solving practices.  The crutch of merely plugging numbers into equations to come up with an answer is of little use.   (There are any number of formulas that relate P, V and T – to know what to use in a particular situation, it is crucial to be able to identify the appropriate approximations and relevant constraints.)  Furthermore , if followed through consistently, thermodynamic reasoning leads to robust conclusions that are independent of the details of microscopic models.  It is for these kinds of reasons that thermodynamics gets a strong recommendation from Einstein:

A theory is the more impressive the greater the simplicity of its premises, the more different kinds of things it relates, and the more extended its area of applicability. Therefore the deep impression that classical thermodynamics made upon me. It is the only physical theory of universal content which I am convinced will never be overthrown, within the framework of applicability of its basic concepts.

Usually I teach the first half of the course that covers the fundamentals – energy, temperature, entropy and the three (or is it four?) laws of thermodynamics.  This year, however, I’ll be doing the condensed matter part of the course.  Here is what I would like to cover, in just 12 lectures:

  • Gibbs free energy
  • First-order phase transitions
  • Thermodynamics of mixing
  • Chemical equilibrium
  • Continuous phase transitions and critical phenomena

That list covers a whole host of phenomena  – from superconductors to why they put salt on icy roads.  But hopefully the common threads will be clear to students.  In fact it can probably be boiled down to two recurring ideas:

  1. free energy (that it should be minimised)
  2. entropy of mixing (that it reduces the free energy)

and even then the second is just an application of the first.

I like to get students to read ahead of the lectures (in fact I quiz them to make sure they do so!).  For most of these topics I’ll  use Schroeder’s excellent book – for its clear and engaging style, focus on the essentials, and well-designed physics problems, even if it mixes in some statistical mechanics and is now over 10 years old.  For continuous phase transitions, it was a little harder to find a suitable book (for second year students), but I think I’ve settled on the opening chapter of an advanced text by Binney et al, “Theory of Critical Phenomena”, mainly because of its excellent motivation; it would be perfect if only its diagrams were a little clearer.

Any good suggestions on what topics to cover and which text to use will most gratefully be considered!