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Statistical Mechanics (and Condensed Matter)

Last update: 13 Dec 2024 22:18
First version: 28 March 1997; substantial edit, 1 April 2003

The first mathematical, natural science of emergent properties. (I hedge this way, because one could argue that economics and evolutionary theory are both, also, concerned with emergent properties --- efficient allocation, and adaptation and speciation, respectively, and they preceeded statistical mechanics.) The heart of the subject is figuring out what happens when vast numbers of particles bounce around and into each other, all obeying the laws of mechanics (classical or quantum as the case may be).

Things I Want to Understand Better: Phase transitions and critical phenoma; the renormalization group; field-theory methods; what happens far from equilibrium (more specifically, are there action principles or the like that govern probability distributions of trajectories, the way thermodynamic potentials govern equilibrium configurations); "soft" condensed matter; biological applications; amorphous materials and glasses; connections between spin glasses and biology (e.g., perceptrons); technical, conceptual and historical issues in the foundations of statistical mechanics.

Recommended:

<rant> If a non-scientist wants to learn about some large and important part of science, say planetary astronomy or genetics, there are usually a handful of reliable, uncontroversial, well-written, non-technical books about it to be found in the stores and libraries, which will convey at least something of the field's history, problems, results and methods. By this point there must be dozens of good popular books written on evolution, particle physics, cosmology, relativity and quantum mechanics, notwithstanding that the last two are about as abstract and abstruse as science gets. There are even excellent popularizations of mathematics, in a continuous tradition from E. T. Bell (if not before). Writing popularizations is an accepted and even encouraged activity for eminent scientists, and has been since Galileo's Starry Messanger. --- Popularizations are also important in the recruitment and education of scientists, but the only one I know of who's written on this is John Maynard Smith, in Did Darwin Get It Right?

A few months ago, when I was trying to explain some parts of my research to my father, I realized I was assuming he knew what statistical mechanics was, and something about how it worked, when in fact he did not. My first thought was to pass on some popular work about statistical mechanics (it's only fair; he did it to me constantly when I was younger). A great many thoughts later I realized I could not think of a single one which didn't stake out some very peculiar philosophical position, or did more than just blab about the second law, never mind something as good as Einstein for Beginners or The First Three Minutes or Does God Play Dice? Granted that relativity and particles and chaos are sexy, and statistical mechanics is not, it's peculiar that there's nothing. Stat. mech. is, after all, one of the essential theories of current physics, actually used by chemists and biologists and materials scientists, etc., the part of physics most directly applicable to daily life (you could illustrate the core of it with a coffee cup, and the whole with a kitchen), and bound up with deep puzzles about why time goes the way it does. This cries out for a remedy.

The undergraduate textbooks on statistical mechanics, like those on most part of physics, are by and large vile. Kittel and Kroemer's Thermal Physics is however decent; if you want a quick-and-dirty guide, and can put up with bad typesetting, try M. G. Bowler's Lectures on Statistical Mechanics. There is nothing analogous to Griffiths's books on electromagnetism, quantum mechanics and particle physics, and if he's got time on his hands...

Chandler's Introduction to Modern Statistical Mechanics is good, as is Landau and Lifshitz's Statistical Physics; the latter is far more comprehensive, but the former is much newer, and easier to learn from. Huang's Statistical Mechanics, one of the other standard texts, is a pedagogic horror.

Having finished this venting of spleen, we turn to the usual list. </rant>

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