# Maxwell’s Demon—A Historical Review

## Abstract

**:**

## 1. Introduction

## 2. Early History

The law that entropy always increases—the second law of thermodynamics—holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations—then so much the worse for Maxwell’s equations. If it is found to be contradicted by observation, well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation [1].—Arthur Eddington

One of the best established facts in thermodynamics is that it is impossible in a system enclosed in an envelope which permits neither change of volume nor passage of heat, and in which both the temperature and the pressure are everywhere the same, to produce any inequality of temperature or of pressure without the expenditure of work. This is the second law of thermodynamics, and it 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.[2]

## 3. Different Demons

While he did not fully solve the puzzle, the tremendous import of Szilard’s 1929 paper is clear: He identified the three central issues related to information-gathering Maxwell’s demons as we understand them today—measurement, information, and entropy—and he established the underpinnings of information theory and its connections with physics.[8]

## 4. Measurement, Information, and Erasure

## 5. Molecular Ratchets

## 6. Photonic Maxwell’s Demon

As the measurement devices are randomized in this process, the experiment cannot violate the second law of thermodynamics.

## 7. Information and Quantum Computing

## 8. Other Recent Work

“…whereas the original photon was part of an orderly train of photons (the laser beam), the scattered photons go off in random directions. The photons thus become more disordered, and we showed that the corresponding increase in the entropy of the light exactly balanced the entropy reduction of the atoms because they get confined by the one-way gate. Therefore, single-photon cooling works as a Maxwell demon in the very sense envisioned by Leo Szilard in 1929.”[31]

We believe that we are still several steps away from a complete understanding of the physical nature of information. First, it is necessary to unify the existing theoretical frameworks, and investigate a comprehensive theory for general processes. Second, we need to verify if other phenomena, such as copolymerization and proofreading, can be analyzed within this unified framework. And third, we must return to Maxwell’s original concern about the second law and try to address the basic problems of statistical mechanics, such as the emergence of the macroscopic world and the subjectivity of entropy, in the light of a general theory of information.[36]

## 9. Conclusions and a Parable

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**This schematic sequence is used to illustrate Maxwell’s demon, following Maxwell’s original description in [2]. In the initial configuration (left frame), the box contains eight gas molecules with a range of speeds. Speeds on the two sides (A and B) follow the same distribution, with some faster and some slower. The right frame shows what happens after the demon (not pictured) uses the trap door between A and B to sort the molecules. After sorting, the faster molecules are in B and the slower ones in A.

**Figure 2.**This schematic diagram illustrates Smoluchowski’s automated pressure demon, described in [4]. The trap door is held loosely in place, perhaps with a spring, so that a molecule approaching from the left can force it open. Some of the molecules coming from the left will, thus, end up on the right side, as shown. The second frame shows that the door mechanism is designed to prevent a reverse flow of molecules, once a density difference between the two sides is established.

**Figure 3.**A box containing a four-molecule gas is divided into equal halves. With two molecules in each half initially (left), the multiplicity of the configuration is Ω = 6. After some time, the system will sometimes evolve to the one shown on the right, with Ω = 1.

**Figure 4.**Now the initial configuration has four molecules on the left (Ω = 1), and the final configuration has two on each side (Ω = 6). An ergodic sample of initial and final configurations includes this result.

**Figure 5.**This is a schematic representation of Szilard’s one-molecule engine, reproduced from [8]. Operation of the engine is described in the narrative.

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Rex, A.
Maxwell’s Demon—A Historical Review. *Entropy* **2017**, *19*, 240.
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Rex A.
Maxwell’s Demon—A Historical Review. *Entropy*. 2017; 19(6):240.
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Rex, Andrew.
2017. "Maxwell’s Demon—A Historical Review" *Entropy* 19, no. 6: 240.
https://doi.org/10.3390/e19060240