Many scientists before Maxwell supported the existence of atoms and molecules, from the ancient determinists Leucippus and Democritus, to Epicurus with his atomic "swerves" that enable free will and the creation of "information structures" in an otherwise chaotic universe, to moderns like Daniel Bernoulli in the 18th century, who argued that the pressure of a gas was the result of atoms bombarding the vessel wall, to John Waterston and John Herapath in the early 19th, whose contributions were largely forgotten, and finally to the great Rudolf Clausius, who stated the Second Law of Thermodynamics in 1850 and introduced the concept of Entropy in 1865, based on the disorderly random motions of gas particles. Clausius introduced the idea of the "mean free path" traveled by a gas particle - in a straight line - between collisions with other particles.

Maxwell's great contribution to the Kinetic Theory of Gases was to find the velocity distribution of the gas particles. Clausius, for simplicity, had assumed that they all move at the same speed. From simple considerations of symmetry and the assumption that motions in the y and z directions were not dependent on motions in the x direction, Maxwell showed that velocities were distributed according to the same normal distribution as the "law of errors" found by Adolphe Quételet in astronomical observations.

Isn't it completely obvious that there is some process at the atomic or molecular level that is randomizing the velocities of atoms and molecules, exactly as ancients like Lucretius and Epicurus thought?.

The only reason to doubt that is the belief of modern scientists that the laws of nature are completely determined, as Isaac Newton's dynamical laws of motion were believed to be. Those laws, including the gravitational force that moves celestial bodies, appear to be determined because they average over vast numbers of microscopic quantum events.

The social physicist Adolphe Quételet and scientific historian Henry Thomas Buckle argued that this distribution applied to social statistics, and scholars have shown that Maxwell's derivation of his velocities distribution followed the derivation the astronomer John Herschel used to explain Quételet's work. ¹

Inspired by the dogma of mechanical determinism that seemed to have been verified by Newtonian physics, Buckle declared that statistical regularities in random human events like marriages, crimes, and suicides, proved that these events were determined and there was no room for human free will.

Maxwell's criticism of his countryman Buckle was clear.

We thus meet with a new kind of regularity — the regularity of averages — a regularity which when we are dealing with millions of millions of individuals is so unvarying that we are almost in danger of confounding it with absolute uniformity.

Maxwell comes close to asserting ontological chance, but he may only be saying one cannot derive determinism from statistical regularities

Laplace in his theory of Probability has given many examples of this kind of statistical regularity and has shown how this regularity is consistent with the utmost irregularity among the individual instances which are enumerated in making up the results. In the hands of Mr Buckle facts of the same kind were brought forward as instances of the unalterable character of natural laws. But the stability of the averages of large numbers of variable events must be carefully distinguished from that absolute uniformity of sequence according to which we suppose that every individual event is determined by its antecedents.²

(Draft Lecture on Molecules, 1784)

Ironically, many scientists and mathematicians, including Laplace himself, were such convinced determinists that they believed the statistical regularities were proof of determinism! Their thinking appears to go something like this:

• Perfectly random, unpredictable individual events (like the throw of dice in games of chance) show statistical regularities that become more and more certain with more trials (the law of large numbers).
• Human events show statistical regularities.
• Human events are determined.

Maxwell would have none of the argument from statistical regularity to determinism. Perhaps because his Christian religion asserted free will, he objected strenuously to the false conclusion. He said he invented his famous demon expressly to show that the Second Law of Thermodynamics has only "statistical certainty." (Letter and Papers, III, Note to Tait 'Concerning Demons,' p.186)

Maxwell asked the question in 1873, "Does the progress of Physical Science tend to given any advantage to the opinion of Necessity (or Determinism) over that of the Contingency of Events and the Freedom of the Will?" (Life of James Clerk Maxwell, p.363)

Maxwell does not discuss the question of whether a particle goes through one slit or the other. But he does see that the light going through both slits has a very strange property. Where light from one slit is bright on the screen, opening the second slit actually darkens a spot that was bright. Is it possible to produce darkness by adding two portions of light? He concludes this cannot be a substance. We now know it is the interference of quantum mechanical probability amplitudes.

There are various methods by which a beam of light from a small luminous object may be divided into two portions, which, after travelling by slightly different paths, finally fall on a white screen. Where the two portions of light overlap each other on the screen, a series of long narrow stripes may be seen, alternately lighter and darker than the average brightness of the screen near them, and when white light is used, these stripes are bordered with colours. By using light of one kind only, such as that obtained from the salted wick of a spirit-lamp, a greater number of bands or fringes may be seen, and a greater difference of brightness between the light and the dark bands. If we stop either of the portions of light into which the original beam was divided, the whole system of bands disappears, showing that they are due, not to either of the portions alone, but to both united.

If we now fix our attention on one of the dark bands, and then cut off one of the partial beams of light, we shall observe that instead of appearing darker it becomes actually brighter, and if we again allow the light to fall on the screen it becomes dark again. Hence it is possible to produce darkness by the addition of two portions of light If light is a substance, there cannot be another substance which when added to it shall produce darkness. We are therefore compelled to admit that light is not a substance.

(Theory of Heat, Chapter XVI, Radiation, Interference.

Note that Maxwell completely understands the sensitivity to initial conditions that is the basis for today's chaos theory

When the state of things is such that an infinitely small variation of the present state will alter only by an infinitely small quantity the state at some future time, the condition of the system, whether at rest or in motion, is said to be stable; but when an infinitely small variation in the present state may bring about a finite difference in the state of the system in a finite time, the condition of the system is said to be unstable.

It is manifest that the existence of unstable conditions renders impossible the prediction of future events, if our knowledge of the present state is only approximate, and not accurate.

It has been well pointed out by Professor Balfour Stewart that physical stability is the characteristic of those systems from the contemplation of which determinists draw their arguments, and physical instability that of those living bodies, and moral instability that of those developable souls, which furnish to consciousness the conviction of free will.

Having thus pointed out some of the relations of physical science to the question, we are the better prepared to inquire what is meant by determination and what by free will.

No one, I suppose, would assign to free will a more than infinitesimal range. No leopard can change his spots, nor can any one by merely wishing it, or, as some say, willing it, introduce discontinuity into his course of existence. Our free will at the best is like that of Lucretius's atoms — which at quite uncertain times and places deviate in an uncertain manner from their course. In the course of this our mortal life we more or less frequently find ourselves on a physical or moral watershed, where an imperceptible deviation is sufficient to determine into which of two valleys we shall descend. The doctrine of free will asserts that in some such cases the Ego alone is the determining cause. The doctrine of Determinism asserts that in every case. without exception, the result is determined by the previous conditions of the subject, whether bodily or mental, and that Ego is mistaken in supposing himself in any way the cause of the actual result, as both what he is pleased to call decisions and the resultant action are corresponding events due to the same fixed laws.

(Essay on Science and Free Will, 1873)

Six years later, Maxwell was intrigued by the work of three Frenchmen, Boussinesq, Cournot, and St Venant, on singular points in the solution of hydrodynamic equations which suggested complete unpredictability of future states. These resembled Lucretius' (really Epicurus') atomic swerves, and they anticipate modern non-linear, deterministic chaos. Although Maxwell did not find the idea really satisfactory, it did challenge the metaphysics of strict causal determinism.

Maxwell wrote in a letter to Francis Galton² (who never responded to the suggestion):

There are certain cases in which a material system, when it comes to a phase in which the particular path which it is describing coincides with the envelope of all such paths may either continue in the particular path or take to the envelope (which in these cases is also a possible path) and which course it takes is not determined by the forces of the system (which are the same for both cases) but when the bifurcation of path occurs, the system, ipso facto, invokes some determining principle which is extra physical (but not extra natural) to determine which of the two paths it is to follow.

When it is on the enveloping path it may at any instant, at its own sweet will, without exerting any force or spending any energy, go off along that one of the particular paths which happens to coincide with the actual condition of the system at that instant.

I think Boussinesq's method is a very powerful one against metaphysical arguments about cause and effect

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.

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 made by one who can perceive and handle the individual molecules which we deal with only in large masses.

In dealing with masses of matter, while we do not perceive the individual molecules, we are compelled to adopt what I have described as the statistical method of calculation, and to abandon the strict dynamical method, in which we follow every motion by the calculus. Let him first observe the molecules in A and when he sees one coming the square of whose velocity is less than the mean sq. vel. of the molecules in B let him open the hole and let it go into B. Next let him watch for a molecule of B, the square of whose velocity is greater than the mean sq. vel. in A, and when it comes to the hole let him draw the slide and let it go into A, keeping the slide shut for all other molecules.

Let him first observe the molecules in A and when he sees one coming the square of whose velocity is less than the mean sq. vel. of the molecules in B let him open the hole and let it go into B. Next let him watch for a molecule of B, the square of whose velocity is greater than the mean sq. vel. in A, and when it comes to the hole let him draw the slide and let it go into A, keeping the slide shut for all other molecules.

Then the number of molecules in A and B are the same as at first, but the energy in A is increased and that in B diminished, that is, the hot system has got hotter and the cold colder and yet no work has been done, only the intelligence of a very observant and neat-fingered being has been employed.

The definition of a demon, according to the use of this word by Maxwell, is an intelligent being endowed with free-will and fine enough tactile and perceptive organization to give him the faculty of observing and influencing individual molecules of matter.

Clerk Maxwell's 'demon' is a creature of imagination having certain, perfectly well defined powers of action, purely mechanical in their character, invented to help us to understand the 'Dissipation of Energy' in nature.

He is a being with no preternatural qualities and differs from real living animals only in extreme smallness and agility. ... He cannot create or annul energy; but just as a living animal does, he can store up limited quantities of energy, and reproduce them at will. By operating selectively on individual atoms he can reverse the natural dissipation of energy, can cause one-half of a closed jar of air, or of a bar of iron, to become glowingly hot and the other ice cold; can direct the energy of the moving molecules of a basin of water to throw the water up to a height and leave it there proportionately cooled...; can 'sort' the molecules in a solution of salt or in a mixture of two gases, so as to reverse the natural process of diffusion, and produce concentration of the solution in one portion of the water, leaving pure water in the remainder of the space occupied; or, in the other case separate the gases into different parts of the containing vessel.

Maxwell confirmed Thomson as the source of the word demon, and explained the demon's purpose.

Concerning Demons.

1. Who gave them this name? Thomson.

2. What were they by nature? Very small BUT lively beings incapable of doing work but able to open and shut valves which move without friction or inertia.

3. What was their chief end? To show that the 2nd Law of Thermodynamics has only a statistical certainty.

• Illustrations of the Dynamical Theory of Gases. I (1860) (velocity distribution)
• Dynamical Theory of Gases. IV (1866)
• Theory of Heat (1871 excerpt)
• On Action at a Distance (Lecture at the Royal Institution)
• Atom (for the Encyclopedia Britannia, 9th edition)
• Essay on Free Will for the Eranus Club (former Apostles)
• Molecules (Published in Nature)
• Paradoxical Philosophy (Review of book by Stewart and Tait)
• Psychophysik (Essay for the Eranus Club)
• Letter to Galton
• Letter to Litchfield