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!

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What’s with the title?

You may be wondering what the title means.  I offer you the following explanations:

  1. Quantata is a reference to physics as the quantitative science par excellence.  As good Popperians, we all know that good science is about prediction in addition to mere explanation.  Hence common pastimes for physicists include predicting the umpteenth digit in the fine structure constant, or searching for minute inaccuracies in Newton’s theory of gravity.  Sometimes this passion for precision even has practical use.
  2. A quantata is a musical celebration of all things quantum. Bach’s well-known  “Coffee Cantata” BWV211 is a somewhat tongue-in-cheek celebration of that divine drink.  Just as a quantum bit has become known as a qubit, a quantum cantata, should someone write one, would no doubt become known as a quantata (because qucantata is just too silly).
  3. Quantata is the plural form of quantum field, as in “Quantum control, quantum computing, and various other quantata promise to usher in a new revolution in technology.”
  4. Quantata is what I made up somewhat in desperation since all the other obvious blog names seemed to have already been taken.  (I have since discovered that I wasn’t the first to make up that word.)
  5. A quantata is a (partially) coherent superposition of all of the above.

The chemistry of the ultracold

All things are made of atoms. That is the key hypothesis

It was Richard Feynman who contended that the most valuable scientific idea was that everything was made of atoms [1].   Knowing that there are different kinds of atoms that can be put together in different ways forms the basis of chemistry, materials science and our understanding of the processes of life itself.  In the other direction, probing the internal structure of atoms has revolutionised our view of the physical world (through the discovery of quantum mechanics)  and has enabled the technology that underpins our civilization – from lasers and electronics to atomic clocks and nuclear energy [2].

But for all the different kinds of atoms that populate the period table, when it comes to the ultracold world [3], there are only two types of atom that matter: bosons and fermions.  You won’t find these listed on the periodic table; but they form the fundamental dichotomy into which all particles can be classified.

(The dichotomy has to do with what happens to the many-body wavefunction when you swap two particles.  If nothings changes, you have bosons.  If the wavefunction changes sign, you have fermions.)

Normal chemistry (at room temperature and one atmosphere of pressure) doesn’t really care whether its particles are fermions or bosons.  But at absolute zero, this is the key distinction that sets the rules of the game, and the periodic table becomes largely irrelevant [4].  Bosons, for example, are gregarious by nature and tend to collect in the same state, forming the matter equivalent of coherent laser light.  Fermions, on the other hand, are rather protective of their personal space, with no two occupying the same state.  What fermions lack in easy-going coherence, they make up for in the propensity to form stable, highly correlated configurations [5].

What determines whether an atom is a boson vs fermion?  It comes down to a simple counting game.  If the number of protons + electrons + neutrons that make up the atom is even, you have a boson, if it is odd, you have a fermion.  Since, for neutral atoms, the number of electrons equals the number of protons, the determining factor is the number of neutrons.

Now here is a thing that I find very strange.  Despite the fact that one extra neutron will radically alter the personality of the atom, the neutrons themselves are locked away within the nucleus, quite inaccessible at ultracold energy scales.  Thus a collection of Lithium-6 atoms behaves entirely differently at ultracold temperatures to a collection of Lithium-7 atoms, despite the two isotopes having almost identical physical and chemical properties [6].  It underlines the point, I suppose, that the ultracold dichotomy of bosons-fermions, and the “chemistry” that derives from it, has nothing to do with interactions between atoms, as in the case of ordinary chemistry, but is a purely quantum statistical effect.

Now on this blog I will try to avoid gratuitously provoking my colleagues by making overreaching claims for the field of ultracold atoms.  But I will say this: The field of optics (or at least the quantum version of it) is preoccupied with photons, which are bosons; the vast field of condensed matter physics arises primarily from the rich physics of electrons, which are fermions.  With ultracold atoms, you can choose which personality you want to deal with, which makes for an interesting playground.

[1] R. P. Feynman, “Six easy pieces”

[2] Less controversial forms of power generation – eg  solar – also depend on knowledge of the internal structure of an atom

[3] where the temperature is measured in nanokelvin, i.e. in thousandths of a degree above absolute zero.

[4] OK, there are some technical reasons to do with cooling and trapping that mean only some candidates from the periodic table are feasible for getting to nanoKelvin temperatures.  Furthermore, the choice of atomic species has consequences for the strength and nature of the interatomic interaction, but these are things that can be controlled by other means (eg external magnetic or electric fields) and are thus not intrinsic to particular kinds of atom.

[5] I hope you’ll forgive the silly anthropomorphism.

[6] Their mass will be slightly different, naturally, but this is just another incidental property.

Why do a PhD in physics?

I recently was asked to speak to a group of potential PhD students about why they would want to do a PhD in physics.  Here are the reasons I came up with:

  1. Curiosity. You’ve just spent the last 4+ years learning about how the universe works based on what others have discovered.  Now it’s your turn to discover something new.  If you’re not fundamentally driven by curiosity about the subject matter, a PhD is going to be a long and difficult road!
  2. Contribution.  You can enjoy that warm fuzzy feeling, knowing that you’re contributing to the sum of human knowledge. The technologies of the future are based on the discoveries of today, including, perhaps, your own.
  3. Skills.  Problem solving, critical thinking, independent investigation, writing: there’s a lot more to a physics PhD than just the maths and the physics.
  4. A job.  A PhD is the minimum requirement for a research or academic career. You won’t ever find someone who tells you that such a career is easy, but plenty will tell you how rewarding it is.  But you don’t have to stick to physics research: there are plenty of other options that would make use of the high level skills you will hone and develop.  Make money working for a bank, or perhaps become prime minister. (The world’s most powerful women has a PhD in physics!)
  5. Travel and meet interesting people.  Somehow physicists arrange to have many of their conferences in very nice locations.  And physicists are interesting, aren’t they?
  6. The title.  If this is one of your main reason for wanting to do a PhD, you should think again!   I admit, however, that it is nice to get the recognition for the hard work, and you might need every scrap of motivation to pull you through those final months of intense thesis-writing.