Szilard Engine

I’m reading Quantum Steampunk by the theoretical physicist Nicole Yunger Halpern. It’s a book about the intersection of quantum mechanics, information theory, and thermodynamics. It’s also aimed at a broad audience, and couched thematically as steampunk. I have little experience with steampunk as a genre – a setting that imagines modern (seemingly magical) technology within the Victorian steam-engine era. I do have some experience with quantum mechanics and statistical thermodynamics since I teach these topics regularly. I have some but not extensive knowledge about information theory.

 

Quantum Steampunk lays the foundation of its three pillars in descriptive terms and evocative examples. You will not find a lot of equations, but you will find some beautifully illustrated figures evoking the Victorian era that Halpern utilizes to help explain the concepts. I was familiar with many of her examples, but one that jumped out at me was the quantum version of the Szilard engine.

 

We discuss Maxwell’s Demon in my statistical thermodynamics class and the possible relation between entropy and information. The Szilard engine is a thought experiment that pushes the idea behind Maxwell’s Demon a little further. Essentially you start with a box with a few gas particles zooming around. Then place a movable partition that bisects the box such that there are more particles on one side than the other, ideally with all the gas particles on one side and none in the other. (This is easier to do with fewer gas particles in the box to begin with.) If your partition is mechanically attached to something that can do work, then as the gas particles on one side push against the partition, the partition moves and you can extract work from the engine.

 

In a two-particle system, your chances of placing the partition in the middle of the box such that both particles are on one side is fifty percent. This Szilard engine can do work. The other half of the time, you’ll trap one on either side, and there is no net work done. A washout. But the quantum version is where things get interesting, and I had not pondered this until reading Halpern’s book. If your two particles are fermions, you always get the washout (Pauli Exclusion Principle!) but if your two particles are bosons, then because of indistinguishability, there’s a one-third chance you get the washout and a two-thirds chance you have a working Szilard engine. It’s an example of where quantum particles can do more thermodynamic work than classical particles. Pretty cool!

 

I enjoyed Halpern’s description of how quantum computing is different from today’s “classical” computing (which does not fundamentally use superposition). She writes in a way that makes the strange nature of quantum mechanics a little more accessible. I say a little more, because (1) no one really understands quantum mechanics, and (2) given I have some background, her writing felt accessible to me but I’m not sure if a non-scientist would agree. Halpern follows-up her Szilard engine description with the Landauer eraser and thus makes the connection to information and entropy. Or I should say entropies. Turns out there a lot of different ways to define entropy. (My students get a sense of this in my classes at a simple level, and we do briefly discuss Shannon entropy.)

 

Thus, the second thing that jumped out at me was Halpern’s discussion on what she calls “one-shot thermodynamics”. I had not heard about this before. It’s been a while since I’ve talked to a hardcore theoretical physicist so maybe that’s why I was ignorant about it. In classical thermodynamics, we rely on averages. When there are zillions (say, Avogadro’s number, applicable to the chemist) of particles in a system behaving “randomly”, then you will pretty much get the average whenever you make a measurement. That’s because that “average” is maximally probably and overshadows all other configurations. Furthermore, if we assume the system is ergodic, that gives us all sorts of other useful mileage which I won’t get into. But what if you just have a small number of particles in your system? Then things get interesting because there’s a small but practically accessible probability that you could extract thermodynamic work which you wouldn’t dream possible in a larger “classical” system. This becomes relevant in quantum systems, and is an example where quantum mechanics allows you to “bend around the Second Law of Thermodynamics” (in Halpern’s words).

 

I’m not sure what to do with my newfound knowledge yet. Much of it is still theoretical although Halpern provides one example in chemistry related to cis-trans isomerism. I haven’t read the relevant papers. This made me think about adding a discussion of the Szilard engine to my P-Chem class and branch a little bit into information theory. I used to do a little more Shannon entropy in the early days but then I found it confused the students on exams, and I’ve since cut back on it. Maybe I should reintroduce the topic given that A.I. and quantum computing are now widespread ideas that most people have at least heard about and might be curious to learn more. So many interesting things. So little time!