Wednesday, August 23, 2017

Tiny Quantum Engines

The previous post mentioned some work on minimal mathematical models for combustion engines, and ended with a link to our first published paper on this subject. That's the paper in which we introduce the class of dynamical systems that we call Hamiltonian daemons. The Hamiltonian part of this name refers to William Rowan Hamilton's formulation of classical mechanics. Hamilton's restatement of all Newton's F = ma stuff dates from 1833 but is still the dominant dialect in physics today, mainly because it adapts well to quantum mechanics.

The daemon part of our name for our systems is partly meant to recall Maxwell's Demon. The devout Presbyterian Maxwell wasn't thinking of an evil spirit: he meant the kind of benevolent natural entity that was the original meaning of the Latin word daemon. Maxwell's daemon was a (purely hypothetical) tiny being who could manipulate individual gas atoms as they flew by him.  Physicists still think about Maxwell's daemon today, as a way to express questions about the microscopic limits of thermodynamics.

Our daemon name is also partly in analogy to Unix daemons, which are little processes that operate autonomously to manage routine tasks without user input. Hamiltonian daemons are mathematical representations of small, closed physical systems which, without any external power or control, can exhibit steady transfer of energy from fast to slow degrees of freedom. In this way they are ultimate microscopic analogs of combustion engines, and learning about them may teach us about the role of thermodynamics on microscopic scales.
A simple Hamiltonian daemon: like a tiny car driving uphill. 

To illustrate how daemons work we took a simple model that resembles a tiny car that tries to drive up an infinite hill. The car's engine has to start in the old-fashioned way of getting it turning by pushing the car, so the car starts out already rolling uphill at some speed. Since it's going uphill, it slows down; some of the time (the dashed curve), the engine fails to ignite and the car just keeps slowing down until it rolls back down the hill. 

Other times, however, the engine catches (solid curve). The car then keeps on driving uphill at a steady speed, expending high-frequency fuel. Since our simple hill is infinite, when the fuel runs out the car will eventually roll back down, but if we add the complication of making the hill level off at some point, the car can climb to the top and then drive on to some goal. 
Schrödinger's Cat as a power source?
More recently we thought, "Hey, really small engines should be quantum mechanical." What would happen if you tried to extract work from a fuel-powered engine that was entirely quantum? What would a quantum Hamiltonian daemon be like? Well, we found out. 

It turns out that the quantum daemon behaves rather like a random daemon. Sometimes the engine ignites, and sometimes it doesn't—even if you do everything exactly the same every time. The quantum daemon also burns its fuel quantum by quantum, and it keeps driving uphill by giving itself a series of kicks that suddenly bump up its speed. After every such kick, there is a chance that the quantum engine will spontaneously stall, and refuse to run further, even if there is fuel left. So over time the quantum probability distribution for the height of the car develops a series of branches, as in the figure here.
The quantum daemon burns fuel in quantized steps, and can randomly stall.

It's not just randomness going on at every kick, though. If you look closely you can see interference fringes in the probability distribution. Since the whole daemon system is closed, the evolution is actually all unitary. Every branch of the figure, which represents a different possible trajectory of the car, is in coherent quantum superposition. Since there is more fuel left if the engine stalls sooner, but less fuel if the engine goes on longer, the superposition of all the branches is a total quantum state with high quantum entanglement between fast and slow degrees of freedom. Since the number of branches grows over time as the quantum daemon operates, the von Neumann entropy of the slow degrees of freedom increases.

Readers who are familiar with quantum mechanics may want to read more in Physical Review E 96, 012119 (2017), or in the free and legal ArXiv e-print version. Our first paper on daemons (Phys. Rev. E 94, 042127 (2016)) is also on ArXiv.

Friday, January 13, 2017

Humphrey Potter and the Ghost in the Machine

Humphrey Potter adds strings to Mr Newcomen's engine so that he can go play.
The first steam engines were slow-working beasts that needed constant human tending. To work its minutes-long cycle, the first Newcomen steam engine needed a human hand to open and close valves for cold water and steam. The machine provided great power, but someone had to control it.

At some point, however, some brilliant mechanical mind noticed that the machine was, after all, creating its own motion. Why not connect the moving piston to the valves, and let the engine run itself?

Some sources even claim to identify the person who first made this brainstorm work: a young boy named Humphrey Potter, who was paid to operate a Newcomen engine by hand. Young Potter hooked up a system of “strings and latches” that made the machine itself do his work for him. Then he ran off to play.

Apparently the sources for this story are not considered reliable. I can’t find any of them myself, and the modern texts that mention Humphrey Potter refer to his story as a legend. That’s a shame, because I’d like to think I could put a name to the person who first made a useful engine run all by itself. 

Apart from the practical advantages of getting a machine to run itself, the scientific point of lazy Potter’s clever trick is that it took any form of intelligence out of the loop of doing work. The entire engine process, from fuel combustion to pumping water, was now a purely mechanical operation. Humphrey Potter banished the ghost from the machine. He made it clear that everything that was occurring, in the marvelous process that turned lumps of coal into useful work, was occurring strictly under the basic laws of physics. It all ran all by itself.

In one way we take this insight for granted now, and may even extend it to processes more complex than lifting weight by burning coal, processes like life and consciousness. Yet in a very practical sense science still has not fully taken the point that engines can run as closed systems, without external power or control, and without any ingredients beyond basic physics. Engineers invoke higher level concepts like pressure and temperature, and while these are clearly valid, they leave a lot of details hidden under the hood. Theoretical physicists analyze parts of the whole process, like how gas particles adapt their motion when a piston moves in a predetermined way, but they do not simultaneously consider how the piston motion is itself determined by the gas particles bouncing off it. We don’t really believe there is any ghost in the machine, but when we have to explain how the machine works, somehow we keep sneaking the ghost back in, in some form or other.

If there's something strange
in your phase space neighborhood ...
At least, until now. Quite recently we have discovered a very simple mathematical model for a minimal kind of combustion engine, that runs as a closed system under basic physics. So we now have a bare-metal, first-principles model for an engine. Its operation is in some ways very reminiscent of a steam engine, but in other ways it is radically different. We are hoping that it may teach us about the microscopic roots of thermodynamics, but someday, perhaps, it might be the basis of a whole new class of power nanotechnology.

Readers who know Hamiltonian mechanics may enjoy our first paper on this subject. "Hamiltonian analogs of combustion engines: A systematic exception to adiabatic decoupling" is published in Physical Review E 94, 042127 (2016), and is also available in e-print form at https://arxiv.org/abs/1701.05006.