Maxwell Demon – Extracting Energy from a System

Energy and thermodynamics

Maxwell's demon is famous for threatening the second law of thermodynamics. But does it? Here we will look at Maxwell original writing, and how we can interpret Maxwell's thought experiment.

Thermodynamics is the branch of physics that deals with energy management. Thermodynamics, like all other branches of science, identifies laws that we believe nature must abide by. Without a doubt, the most important law of thermodynamics, is the second.

There are various statements that derive from the second law. The simplest and most intuitive of these states that it is impossible for a heat engine to produce energy if it exchanges heat only with bodies at a single fixed temperature.

To understand the second law, let us consider a simple engine, consisting of two heat reservoirs and a piston in a cylinder full of air. Imagine one moves the piston from one reservoir to the other. If the reservoirs are at different temperatures, the air in the cylinder expands and contracts. This drives the piston up and down, just like a piston in a steam engine or an internal combustion engine.

But if the two reservoirs are at a single fixed temperature, the volume of the gas is the same. This means the piston does not move up and down when we move the cylinder. If someone could invent a way to produce energy using such a system, they’d have solved humanity’s energy problems. We could in fact take two points in the sea and use them as "reservoirs". In this way, we could transform part of the thermal energy stored in the ocean into mechanical energy.

The second law of thermodynamics states that this is impossible.

But is it?

The little demon

In the late 1800s, Clerk Maxwell was laying the cornerstones of physics. But he also appeared to challenge the second law in a "thought” experiment. Maxwell does not speak about a demon in reality, and winds up his “Theory of heat” as follows:

“… the second law of thermodynamics … is undoubtedly true as long as we can deal with bodies only in mass, and have no power of perceiving or handling the separate molecules of which they are made up. But if we conceive a being whose faculties are so sharpened that he can follow every molecule in its course, such a being, whose attributes are still as essentially finite as our own, would be able to do what is at present impossible to us.

For we have seen that the molecules in a vessel full of air at uniform temperature are moving with velocities by no means uniform, though the mean velocity of any great number of them, arbitrarily selected, is almost exactly uniform. Now let us suppose that such a vessel is divided into two portions, A and B, by a division in which there is a small hole, and that a being, who can see the individual molecules, opens and closes this hole, so as to allow only the swifter molecules to pass from A to B, and only the slower ones to pass from B to A. He will thus, without expenditure of work, raise the temperature of B and lower that of A, in contradiction to the second law of thermodynamics.”

Maxwell concludes by explaining that his theory does not necessarily clash with the laws of thermodynamics: “This is only one of the instances in which conclusions which we have drawn from our experience of bodies consisting of an immense number of molecules may be found not to be applicable to the more delicate observations and experiments which we may suppose are made by one who can perceive and handle the individual molecules”

Maxwell and Socrates' demons

In practice, Maxwell says: "We cannot know the velocity of each molecule. Therefore the second law is valid for the macroscopic world". The second law is a “statistical” law. It is valid if we consider many molecules as if they were one single body. We use statistical instruments because we do not have sufficient information on the position of each single molecule. We are ignorant.

But you won’t find many who agree with this. Maxwell’s door-opening being was called a “demon”, a very appropriate name. The city accused Socrates of believing more in his own personal demons than in the Gods. Maxwell was attacked merely for having dared to imagine his demon challenging the "divine laws" of thermodynamics.

In reality, Maxwell was only recognising his (and our) ignorance. And like Socrates was attacked for that: the city indeed accused Socrates of believing what the oracle of Delphi said, that he was the wisest of all men. And he explained he actually believed he was the wisest because he was the only one recognising and accepting his own ignorance: "I am better off than he [a conceited politician] is - for he knows nothing, and thinks that he knows. I neither know nor think that I know. In this latter particular, then, I seem to have slightly the advantage of him".

Attacking the demon

On 28 February 1879, Lord Kelvin gave a lesson at the Royal Institution. Soon later, the American Popular Science Monthly published this editorial: “There is a certain class of minds whose efforts to explain things generally leave them more obscure than they were before. … A marked illustration of this is afforded by a lecture delivered … by the eminent physicist and mathematician, Sir William Thomson [Lord of Kelvin], who announced as his topic of discourse the curious subject, ‘Maxwell's Sorting Demons.’”

The editor of the American monthly, today published as Popular Science, didn’t really understand Kelvin’s lesson. He thought Maxwell used the demon to explain diffusion processes. ??.

In his confused interpretation, the editor stumbled on something that scientists later connected to the demon: the demon had a hand in “the origin of terrestrial life”.

The concept of the demon, in fact, seems to suggest that the origin of life derived from the capacity to take another approach to nature and therefore extract energy in ways in which other, less capable beings, had failed.

But how can this have been possible? Does the second law only apply to us, but not to microscopic life forms?

It was actually the concept of entropy that required more in-depth study, and Maxwell’s note on the differences between macroscopic and microscopic is crucial.

Entropy and probability: what is the connection? (future post)

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