This week’s BMC post will be a bit of a short, focused post about phase transitions and a nifty mathematical tool for looking at how they behave. I’m in the foggy head space of 4 hours of sleep right now, so forgive me if this is less of a science primer and more the ramblings of a madman.
So, today’s BMC post will touch on a topic near and dear to all my readers hearts: magnets, how do they work? Well, dear reader, they are not in fact miracles, but the result of the interactions of spin lattices that can be described using the Ising model of magnetism. I shall endeavor to explain a few key features of this model to you, and let you know about a few cool things we can do with it. Continue reading
We’ve discussed in a couple of the past BMC posts the difference between Bosons and Fermions, and the degenerate states that fermions can form. Well, today I’m going to talk about something that you may have heard of, but probably have never had explained to you: Bose-Einstein Condensation. I’ll tell you a bit about what it is, and tell you about a cool application of them: atomtronics.
In some of the past BMC posts, I have blogged about how statistical mechanics, in the 19th century, came perilously close to uncovering quantum mechanics early. A number of “problems” with statistical mechanics arose due to the classical treatment used. One of the most serious was the Ultraviolet Catastrophe. This problem was not easily solved with the hand-wavey pseudo-quantum explanations used in some previous cases. It took a full-on, quantized description of electromagnetism, and helped usher in quantum mechanics to being the foremost theory in subatomic physics.
I was just reading some of Ted Chiang’s excellent short story collection “Stories of Your Life and Others”, and was reminded of a story of his I read much earlier, Exhalation. This Hugo-winning short story didn’t just catch my imagination and sense of wonder (something that a good Sci-Fi writer can do extremely well in the short format) like Asimov’s Last Question, but also is a wonderful pedagogical tool for explaining thermodynamic concepts. I won’t blow any of the fascinating world that Chiang built, but I will tell you that the final revelation the protagonist faces is a perfect illustration of the Second Law of Thermodynamics. This story is such a good way of explaining it to people, precisely because it is a story. Any skeptic or psychologist can tell you that the emotional connection a good story provides is among the most effective ways of compelling people (after all, what is mythology but a good collection of stories?). So, in other words, go read his story here:
So, in last weeks BMC post, I showed a number of probability distributions, one of which was the Fermi distribution. As you saw, at low temperatures, the Fermi distribution approached a step function. This itself was a bit weird, as it implied that there are particles in non-zero energy levels even when the temperature is zero. This distribution’s shape produces a number of bizarre properties, the great fun pop-science kind of things that makes physics popular among you, the unwashed masses (I kid, I love this stuff too).
So, for today’s BMC post, I’m going to be attacking a topic from a different angle. I’d like to show you all about thermodynamic distribution functions (mathematical functions that describe the number of particles across a range of some property). However, rather than simply explaining the properties to you in text, I’d like to tell you what the distributions describe, and then see what kind of properties we can derive from looking at the shape of the functions.
So, I’ve already made you, dear reader, somewhat familiar with entropy (if not, go back and read this post). I have bad news, I am afraid: I LIED. But trust me, I had only the best intentions! The definitions I have given in the previous post are still completely correct, but simplified too far. The problem that arises from the old post is called the Gibbs Paradox, and I will in this post explain what this is, and how it is rectified.