John Baez’s Week 235 of This Week’s Finds in Mathematical Physics is out. This week he talks about quantum computing, and his work on higher gauge theory.
Bee at Backreaction has written the definitive weblog post on the experimental search for evidence of the existence of extra dimensions. (One consequence of string theory, if it’s true, is the existence of additional dimensions beyond four.)
Rob Knop thinks that the Big Bang is a bad name for a good theory. Read this post on his weblog for more. If astronomers ever do decide to drop the name Big Bang, I hope they return to Lemaitre’s original name for the concept: the primordial atom. It has a 20s-science-fiction/evil-scientist sound to it. You can just imagine Bela Lugosi saying, “The fools. They laughed at me, but they’ll laugh no more once I have harnessed the power of the primordial atom”.
I saw a story on Cosmic Variance that I found vaguely shocking. At the SUSY06 conference, there was a rancorous discussion about whether the data from the Large Hadron Collider should be made public. This is probably my ignorance about how high-energy physics works, but I have trouble believing that the answer is anything other than “of course” (perhaps after an embargo period to reward the people actually working on the detector). Some good news that comes out of the comment thread is that in astronomy such public data is readily available.
Scott Aaronson has posted an extremely funny parable on his weblog about physicists and impossibility proofs.
Week 234 of John Baez’ This Week in Mathematical Physics is up. Most of this week’s edition is about the relationship of mathematics and music, but he does touch on a topic we’ve discussed before: weird orbits in classical mechanics. Cris Moore and Michael Nauenberg have found many new and strange solutions to the n-body problem and have provided movies (animated GIFs). The most amazing one is 21 bodies all moving along the same figure eight orbit.
I’ve been poking around Cosma Shalizi‘s website recently. He has a little bit of everything: a weblog, a set of book reviews he’s written, and a large collection of mini-essays (which he calls “notebooks”). The bulk of the material revolves around the related subjects of probability, machine learning, and dynamical systems (all with a strong physics flavor), but he touches on many other topics.
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.)
Something I’d always meant to do is learn something about thermodynamics. I’ve tried several times, but each time I get bogged down in the details of heat engines. This time, I found some very nice lecture notes by Nino Boccara. They provide an overview abstracted enough from the physical details to be informative to a mathematical audience. They take entropy as a primitive concept rather than deriving it from properties of heat engines.
(I’ve been trying to find other introductions from the same point of view of Boccara, but with more detail. I haven’t had any luck. Rather than sticking closely to ideal gases, Boccara takes a general view of the formalism, one that does not (in principle) even require energy as one of the state variables. His approach to statistical mechanics is related to the maximum entropy approach of E. T. Jaynes.)