Almost all of modern physics comes down to understanding steam engines. Yes, we have all sorts of fancy laws about the Universe and atoms, but thermodynamics rules them all (and not in Sauron’s benevolent dictatorship style). When thermodynamics slaps you, you feel it. In a new theory paper, a pair of physicists have risked a slapping by nature.
Carnot rules
One famous limit of thermodynamics is that heat engines, like steam engines and internal combustion engines, must be less efficient than a Carnot heat engine (a heat engine cycle designed by French engineer Carnot). Although the Carnot efficiency is very easy to calculate, building an engine that operates at that efficiency is highly impractical.
It’s not just the impractical mechanics of such an engine. The very nature of the engine suggests that the ideal operating efficiency is achieved only for zero output power. Not very useful, in so many words. But it gets even less useful than that. By delving into the details, you find that as the output power approaches zero, the fluctuations in output power get very large. In other words, even if we could construct such an engine, it would run erratically and drive the operator insane.
The source of the problem lies in how all heat engines work. Work is done by taking heat from a reservoir of energy (a heat source) and delivering it to a cold region, extracting energy on the way. The heat energy is delivered by particles or waves; in both cases, the trajectory they follow through the energy landscape is random. Only on average do they follow the trajectory described by Carnot.
As our output power drops (and we get closer to the Carnot efficiency), the number of particles delivering energy reduces to just one or two undergoing the cycle at any one time. So the energy per unit time is given by the individual path of these one or two particles, which may be very different from the average. Hence, the power per time fluctuates. In an ideal engine, these fluctuations hit infinity as the average delivered power hits zero, which is where the average efficiency reaches the Carnot efficiency.
The reciprocating Carnot
These results, however, are for a heat engine that operates continuously. What about an engine that operates cyclically? It turns out that cycling the engine enables a pair of remarkable properties. First, it seems that the engines might be practical—we will get to what that means in a bit—even though they use the same set of thermal operations as a Carnot engine.
Cyclic heat engines seem to deliver a non-zero amount of energy in a finite time. In fact, they do better than that—their output power can be quite high if the power fluctuations become small. In the case of the fluctuations going to zero, the engine would operate at the Carnot efficiency.
Power delivery depends on reducing fluctuations, but it turns out that a cyclical heat engine will do that, too. The researchers show that the fluctuations do not become larger as the total output power drops. Instead, they flatten out to some finite value.
Why does this happen? I think it’s a bit of sleight of hand. In a steady-state heat engine, the operating conditions demand that we have only a small number of particles following the thermodynamic trajectory at any one time. We are subject to large fluctuations in power since the particles follow random paths. But if we cycle, there are periods of time when there are absolutely no particles in the system, and to make up for that, there must be more during the cycle, meaning their collective behavior gets closer to the average.
To summarize, what we have now is not a heat engine with zero average output power and large random fluctuations. Instead, we have a heat engine that has large known fluctuations (the output during the cycle) separated by known periods of zero output power.
A practical cycling Carnot?
I said that the engine is practical, and I stand by that statement. Engines have many uses and are found in unusual places. For instance, enzymes are a type of engine that do work based on chemical reactions. They are still subject to Carnot efficiency. They, and other micro-machines, are also engines that are more likely to be able to cycle and therefore get close to Carnot efficiency.
The researchers also calculated that their engine could be demonstrated using something like a glass bead held by optical tweezers. The optical tweezers can be used to do work on the bead with a cycle initiated externally by changing the laser power or focal conditions.
These may not be things that come to mind when you think of engines. But they are practical. Especially now, when we are staring at a future full of micro-machines and enzymes that produce everything from food to fuel.
Physical Review Letters, 2018, DOI: 10.1103/PhysRevLett.121.120601 (About DOIs)
