What triggered my current plunge into thermodynamics was this miniature book review by Cosma Shalizi of Richard S. Ellis’ Entropy, Large Deviations, and Statistical Mechanics:
In addition to being an excellent exposition of the rigorous theory of large deviations (especially for physicists, naturally!), this is also one of the most conceptually satisfying approaches to the foundations of statistical mechanics. In particular, it makes good probabilistic sense of the method of maximum entropy, without invoking weird sub-Bayesian ideas about statistical inference. (Namely, maximum Gibbs-Shannon entropy drops out as an approximate consequence of large deviations theory, when considering a small part of a large system, becoming exact only in the thermodynamic limit. As Ellis says, the core of this idea goes back to Boltzmann.)
I find the idea of statistical mechanics fascinating: that to describe the behavior of truly gigantic numbers of particles, all we need are a few bulk properties such as temperature and pressure. And to find out that it has a simple mathematical description in terms of probability theory, that’s the kind of thing that makes me want to know more.
Tragically, my library doesn’t have Ellis’ book, but I was able to track down home page, which has an extensive list of publications, many of which are available on-line. Two in particular give an overview of the relationship between statistical mechanics and large deviations:
- The Theory of Large Deviations: from Boltzmann’s 1877 calculation to equilibrium macrostates in 2D turbulence
- An Overview of the Theory of Large Deviations and Applications to Statistical Mechanics
Cosma also has a quick intro to large deviations. (In a rare lapse, Wikipedia has almost nothing. All that’s there is a pathetic little stub that I just created to fix what was there before, which was an incorrect redirect to extreme value theory.)