Jeans, Donnan, Guggenheim debate

Jeans debate
The Jeans, Donnan, Guggenheim debate was a Jan to Aug 1934 debate, taking place via an exchange of letters in Nature, between James Jeans, whose book The New Background of Science (1933) defines, as a matter of fact, “life” to be characterized by the ability or capacity to evade the second law of thermodynamics, and Frederick Donnan and Edward Guggenheim, who oppose this view.
In debates, Jeans, Donnan, Guggenheim debate (TR:8), aka dialogue on "Activities of Life and the Second Law of Thermodynamics", refers to a Jan to Aug 1934 debate on the question of whether "life" is has the capacity or is defined by the capacity to "evade" the second law of thermodynamics, between English mathematical physicist James Jeans, who is for the position, per some closeted theism and or anthropism reasons, and Irish physical chemist Frederick Donnan and English physical chemist, physicist, and statistician Edward Guggenheim, who both oppose the conjecture, the dialogue of which taking place via an exchange of letters in Nature.

Jeans | 1933
In 1933, James Jeans, in his The New Background of Science, following passing references to god, e.g. “from the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician”, stated that, as a supposed matter of fact, that life is defined by its ability to evade the second law of thermodynamics; the exact quote is as follows:

“In fact, it would seem reasonable to define life as being characterized by a capacity for evading this law. If probably cannot evade the laws of atomic physics, which are believed to apply as much to the atoms of a brain as to the atoms of a brick, but it seems able to evade this statistical laws of probability. The higher the type of life, the greater is its capacity for evasion.”
— James Jeans (1933), The New Background of Physics (pg. 280) [1]

The full 15-page section, which opens chapter 8, on "events", devoted to thermodynamics and the "activities of life", in which the above debate-provoking quote is found, is as follows:



The province of atomic physics is to discuss the nature of particular events, and it has been very successful in showing us how it is that certain kinds of events occur, while others do not. Yet this can give us but little information as to what is happening to the universe as a whole. Another branch of physics, known as thermodynamics, takes this problem in hand; it does not concern itself with individual events separately, but studies events in crowds, statistically. Its province is to discuss the general trend of events, with a view to predicting how the universe as a whole will change with the passage of time
Jeans (contents)
The contents to James JeansThe New Background of Science (1933), wherein he attempts to present the new wave-particle duality view of the universe as the “new background” view of science, but after his “Indeterminacy” (§7) chapter, wherein Heisenberg uncertainty principle is introduced, thereafter selling a metaphysical indeterministic platform, in his “Events” (§8) chapter, he devotes a section to “Entropy”, at the end of which provocatively claiming that living things have the ability to "evade" the second law of thermodynamics. [1]

The science of thermodynamics had its origin in severely practical problems relating to the efficiency of engines, but it was soon extended to cover the operations of nature as a whole. All this happened in the days when nature WAS assumed, without question, to be mechanical and deterministic. In what follows, we shall not treat nature as mechanical, but for the moment we shall treat it as though it were strictly deterministic.

On a deterministic view of nature, the universe never has any choice; its final state is inherent in its present state, just as this present state was inherent in its state at its creation. It must inevitably move along a single road to a predestined end, like a train rolling along a single-track line, on which there are no junctions of any

(pg. 261)

kind. Thus, if a ‘super-experimentalist’ [see: Holbach's geomatrician] could discover the exact position and the exact speed of motion of every particle in the universe at any single instant, a ‘super-mathematician’ would be able to deduce the whole past and the whole future of the universe from these data.

Experimental physics has not yet been able to provide such data, and the uncertainty principle shows that it never will be. Yet a ‘super-mathematician’, who had unlimited time at his disposal, might calculate out all the different pasts and futures which would result from all conceivable sets of data — in other words from all conceivable present states.

He might commence his labors by making a diagram in which to map out all possible states (Ѻ)(Ѻ) of the universe, just as all points in England are mapped out in an ordinary geographical map. He could start from any particular point in this diagram and trace out, by mathematical calculation, the whole future of a universe which started from the state represented by this point. He could represent this future by a line through the point, which would run through his diagram much as a railway line is represented by a line running across the map of England. He could take point after point in his diagram in turn, and represent the development of a universe which started from each point by a line, until his whole diagram was filled with lines. These lines would represent all the lines of development which were possible for the universe. If the universe was strictly deterministic, as we have so far supposed, the diagram would look like the map of a country covered with single-track lines of rail-way, with no junctions of any kind. If, on the other hand, strict determinism does not prevail in the universe, there

(pg. 262)

may be any number of junctions and connecting tracks between the different lines.

Let us imagine that a perfect diagram of this kind is at our disposal, as it would be — in theory at least — if we had a perfect knowledge of the laws of nature. No matter how perfect the diagram is, we are still unable to gain a detailed knowledge of our future from it, because we do not know our present position on the map. This makes it impossible to identify the particular track on which we are travelling, so that we can neither say what part of the diagram it will traverse next nor where it will end. Yet it may be possible to discover in what kind of country it ends, and this is the information we really want. It is information of this kind that the science of thermodynamics can provide.

Imagine that we suddenly waken up from a state of unconsciousness to discover we are on a British railway. We have no means of knowing where our journey will end. Yet if we have a physical map of Great Britain with us, we may notice that only a few hundred acres out of 55 million lie as much as 4000 feet above sea-level. Although we cannot say where our journey will end, there are obviously very long odds that it will end at a height of something less than 4000 feet above sea-level. If a barometer in our compartment indicates that we are already as much as 4000 feet above sea-level, then there are very long odds that the general trend of our journey will be downhill.

It is to considerations of this kind, rather than to exact knowledge, that we must turn for guidance in our efforts to study the evolution and final end of the universe. As certain knowledge is beyond our reach, we must be

(pg. 263)

guided entirely by probabilities. Yet the odds we encounter in calculating these probabilities prove always to be so immense that we may, for all practical purposes, treat long odds as certainties. Because the number of particleselectrons and protons — in the universe is of the order of 10^79, we find that high powers of 10^79 enter into all our odds, and, this being so, we need not trouble to differentiate too carefully between probabilities of such a kind and certainties.

§§: Entropy

Thermodynamics is much concerned with a quantity known as ‘entropy’. This plays much the same part in our diagram of the universe as height played in our imaginary railway map of Great Britain, except that small entropy corresponds to great height, and vice-versa [large entropy corresponds to great depth]; thus entropy does not correspond so much to height above the level of the sea, as to depth below the top of the highest mountain. The highest mountain in Great Britain rises to 4400 ft above sea-level, and as most of Great Britain is only a little above sea-level, most of it is at a depth, in this sense of the word, of nearly 4400 ft — the maximum depth possible. In the same way, we find that most of the configurations which figure in our map of the universe are at the maximum entropy possible — all, indeed, except for minute regions whose sizes are proportional to inverse powers of 10^79.

At the moment we cannot justify this statement because we have not yet defined ‘entropy. And there is no need to justify it, because the best definition of ‘entropy’ makes the statement true of itself and automatically. It is convenient to define ‘maximum entropy’ as specifying

(pg. 264)

the condition which is commonest in our map of the universe, and then, having done this, to define entropy in general in such a way that the more common condition is always of higher entropy than the less common. Thus, we define entropy to be a measure of the ‘commonness’ of a given state in our map. If W is the ‘commonness’ [see: multiplicity] of a certain state, the mathematician defines the entropy of this state as:

Entropy = k log W

where k is the gas constant [see: Boltzmann constant]. With this definition we find that, just because the numerical factors involved are so immense, conditions of ‘maximum’ entropy are not only more common, but incomparably more common, than those whose entropy is less, and so it is all down the ladder. Because of this, it is practically certain that each state of the universe will be succeeded by a state of higher entropy than itself, so that the universe will ‘evolve’ through a succession of states of ever-increasing entropy, until it finally reaches a state of maximum entropy. Beyond this it cannot go; it must come to rest — not in the sense that every atom in it will have come to rest (for maximum entropy does not involve this), but rather in the sense that its general characteristics cannot change any more.

Yet if someone asserts that this will not happen, and that the universe will move to a state of lower entropy than the present, we cannot prove him wrong. He is entitled to his opinion, either as a speculation or as a pious hope. All we can say is that the odds against his dream coming true involve a very high power of 10^79 his disfavor.

Thermodynamics is accustomed to disregard all such infinitesimal chances and forlorn hopes, and announces its laws as certainties. We must nevertheless always bear in mind that there is a small risk of failure attached to

(pg. 265)

every such law. The famous ‘second law of thermodynamics’ asserts that the entropy of a natural system always increases, until a final state is attained in which the entropy can increase no further; a fuller statement of the law would be that the chances of the entropy doing otherwise are negligibly small.

§§: The Final State of Maximum Entropy

We now see that the question of discovering the final state of the universe is merely that of discovering how far the entropy of the universe can increase without violating the physical laws which govern the motions of its smallest parts. There was no need to take the physical properties of matter into account in defining entropy, but we must do so before we can discover the state in which the entropy is a maximum.

The process is usually very complicated, but two simple instances may illustrate the general characteristics of a state of maximum entropy. They do not refer to the universe as a whole, but merely to minute portions which have been selected for their simplicity and familiarity.

Let us pour some red ink into water, and leave the ink and the water to diffuse into one another. We know, before the event occurs, that the final state will be one in which they are uniformly mixed to form a homogeneous pinkish fluid, and as this state of uniform mixture is invariably the final state, we know that it must be the state of maximum entropy.

Again, let us put a kettle of cold water over a hot fire. We know, before we perform the experiment, that the final state will be one in which all the water is turned into steam. This also must be a state of maximum entropy.

(pg. 266)

Just as the red ink diffused itself equally through all parts of the water in attaining a state of maximum entropy, so the heat of the fire tends to diffuse itself equally through coal, kettle, and water.

These instances have shown us two final states in which the entropy is a maximum. They illustrate a very wide and very general principle — the final state of maximum entropy avoids concentration, whether of special sub-stances (as with the ink) or of energy (as with the heat of the fire). The ‘commonest state’ is one in which both substance and energy are uniformly diffused, just as the commonest state in which we find a concert audience is that in which tall people and short, dark and fair, and so on, are uniformly diffused.

General considerations of this kind can tell us something at least as to the final end of the universe, but they cannot indicate the road by which it will be reached. All they can tell us is that the road is practically certain to be one of increasing entropy throughout; and the better we understand entropy, the more this statement will convey to us. It is not impossible for the entropy to decrease, but it is almost infinitely improbable that it should do so.

For instance, when the ink and water have once become thoroughly mixed, the state of maximum entropy has been attained; the ink-water mixture cannot change its general characteristics any further without a decrease of entropy. Yet the molecules of ink and water still jostle one another about, and change places as they do so. It is quite conceivable that their random motions should take them into a configuration in which all the ink molecules are found at one end of the vessel, and all the water molecules at the other. The entropy of such a configuration

(pg. 267)

is far below the maximum possible, so that the odds against the molecules of ink and water assuming such a configuration are immense. Yet it is important to notice that no law of nature prohibits it. Indeed, if we had an infinite number of vessels of ink and water, the unexpected would be bound to happen in a few of them — just as, if an enormous number of hands of bridge are played, there are bound to be few deals in which each player gets one complete suit, in spite of the immense a priori odds against such an event occurring in a single individual case. The event is bound to occur either if an enormous number of players play bridge for a short time or if a single party of players play for an enormous time. In the same way we may say that a complete separation of the ink and water is bound to occur, either if we have an infinite number of vessels containing the mixture, or if a single vessel exists for an infinite time.

Similar considerations apply to our other miniature universe of fire, kettle and water; the water in the kettle may freeze as the result of being put over a hot fire [?]. To prove this, we need only notice that there is a possible state of this group of objects in which the water exists in the form of ice, and the fire is even hotter than before because there is less heat in the kettle and its contents. If we map out all the configurations of the system, this particular configuration must appear on the map, so that we cannot know for certain that it will not be the end of the journey. We know, however, that when we put a kettle of ice on the fire the normal event is for it to turn into a kettle of water. This shews that the entropy of the water-configuration is higher than that of the ice-configuration, and this in turn shows that although it is

(pg. 268)

possible for a kettle of water to freeze when placed over a hot fire [?], it is almost infinitely improbable that it will do so on any single occasion. If even the most credible of witnesses told us a kettle of water had frozen when he put it on a hot fire, we should not believe him, although there is nothing in the laws of nature to prohibit such an occurrence [?]; indeed these very laws assure us that the event must occasionally happen. Yet such occasions must from the nature of things be so very rare, that we should think it far more likely that our informant had gone crazy, had been deceived, or was lying, than that he had been present at one of them.

These examples have both illustrated cases in which the individual atoms and molecules are left to perform random motions under the play of blind forces. If the atoms and molecules receive any kind of guidance [?], the result may be very different. Suppose that, instead of ink, we pour oil into our water. We no longer expect the final result to be a uniform mixture; we know that we shall find all the oil on top and all the water below. An arrangement which is inconceivably improbable for ink and water is found to be the most probable of all for oil and water; indeed, exact calculation confirms that a state of practically complete separation is the state of maximum entropy in the case now under consideration. The reason for the change is that the force of gravity differentiates between the molecules of oil and of water. When we say that oil is of lower specific gravity than water, we mean in effect that the earth's attraction draws particles of water downward with a force greater than it exerts on equal-sized particles of oil. Because it continually drags these latter particles down with a smaller force, it encourages

(pg. 269)

them to move upwards through the water. When we mix oil and water, we are not handing over their molecules to be the playthings of a blind chance, but rather to a chance over-ridden by the selective action of gravitation. There is blind interplay of the molecules of oil between themselves and of the molecules of water between themselves, but the cross interplay is controlled by gravitation.

Suppose, for instance, that we divide our vessel into two equal divisions, each holding a pint, by a horizontal membrane with a small pinhole in it. Let us mix a pint of oil and a pint of water as thoroughly as possible, and fill our vessel on both sides of the membrane with this quart of mixed liquid. After a sufficient time, we shall of course find that all the oil has passed into the upper half, while all the water has passed into the lower half; our careful mixing has been undone, and this by very simple means. Whenever a particle of oil in the lower half met a particle of water in the upper half at the pinhole — the only place at which they could meet — the force of gravity urged them to change places, and such interchanges have continually increased the amount of oil in the upper half and that of water in the lower half, until complete separation has been effected.

§§: The Sorting Demon of Maxwell

If we performed a similar experiment with our previous mixture of water and red ink, no such action would take place in the ordinary course of nature, since gravity makes no distinction between liquids of the same specific gravity. Yet suppose an intelligent being of microscopic size were placed at the pinhole, armed with a tiny shutter with which he could dose the aperture when he wished, and

(pg. 270)

was given instructions to open it only for molecules of ink passing upwards or for molecules of water passing downwards — in brief his task would be to perform a selective action like that which gravity performs for oil and water. It is clear that after a long enough time the ink and water will be as thoroughly separated as the oil and water had previously been, although this time the separation would have been produced not by gravity but by intelligence.

The intelligent microscopic being we have just described was introduced into science by the Cambridge physicist James Maxwell, and is generally described as ‘Maxwell's demon’. The demon, we must notice, in no way sets himself in opposition to the laws of mechanics. We do not know how often he finds it necessary to open and close his microscopic shutter. The natural motions of the molecules may conceivably be such that he finds no occasion to close it at all. Then everything will go on precisely as though the demon had not been called on to help, the ink and water separating out under their own natural random motions. Yet the odds against such an occurrence are unthinkably large. As each separate molecule comes into view, the demon must ask himself the question ‘To act or not to act?’, and then put his decision into practice. A prolonged run of decisions all in the same sense will be as improbable as a prolonged run of heads or of tails when we spin a coin. Thus, it is exceedingly unlikely that our demon will find that no action is needed time after time; the normal event will be that he will need to open and close his shutter millions of times. Even so, he expends no energy in so doing [?], and each time the shutter is closed against a molecule, we may reflect

(pg. 271)

that had the path of the molecule in question been a hair's-breadth to right or left, it would have bounced off the membrane without the demon touching his shutter.

Although the demon does not interfere with the operation of the laws of nature, yet he exercises a selective effect, and by this alone he can cause any system to pass to a state of lower entropy [see: low entropy state]. Natural forces, left to their own blind interplay, are practically certain to increase the entropy, but it is the play of the laws of probability rather than of the laws of nature that produces this result. The demon has not been told to circumvent the laws of nature, but the laws of probability; he can so to speak load the dice from moment to moment, and obtain any result he wants provided this does not violate the laws of nature — the conservation of mass, of energy, and so forth. When red ink and water are mixed, he cannot increase the total amount of either or both; all he can do is to disentangle them, as one might sort out a heap of red and white beads, or again as a railway shunter divides up a goods train by moving the switches in different ways for different wagons. When a kettle of water is placed over a fire, he cannot add to the total amount of heat, but he can, if he wishes, increase the heat of the fire by subtracting heat from the kettle. His accomplishments are limited to robbing Peter to pay Paul (Ѻ), whereas unaided nature would leave Peter and Paul to fight it out — or perhaps to toss up for it time after time.

Quite general considerations shew that the universe as a whole has a very long way to go before coming any-where near its final state of maximum entropy. In this final state, concentrations of radiation and of temperature will equally have disappeared, so that radiation will be

(pg. 272)

distributed uniformly throughout space, and the temperature will be everywhere the same. At present, the density of radiant energy out in the farthest depths of space corresponds to a temperature of less than one degree above absolute zero; in the interstellar spaces of the galactic system, to three or four degrees only; near the earth's orbit to about 280 degrees; at the sun's surface to about 6000 degrees; at the sun's centre to perhaps 40 or 50 million degrees. The universe can always increase its entropy by equalizing these temperatures; as for instance by letting energy flow from the sun's hot centre to its cooler surface, by letting it then stream out into space, past the earth's orbit, into the cold and dark of interstellar and intergalactic space. There can be no end to the increase of entropy until these regions are all at the same temperature, with radiant energy diffused uniformly throughout space. Then, and then only, will the universe have reached its final state, a state in which the temperature will everywhere have fallen too low for life to exist —the perfect quiet and perfect darkness of eternal night.

§§: The Activities of Life

A general survey of the universe as a whole suggests that it is rapidly moving towards such an end. The sun is dying, pouring out some 250 million tons of its substance in the form of radiation each minute, thereby lowering its own heat and raising that of empty space. Other stars tell the same story; we find no evidence of sorting demons sitting on their surfaces to turn the heat back into their hot interiors. Yet a being from another universe [see: advanced intelligence] who scrutinized this earth of ours with sufficient care might notice signs which led him to wonder whether there

(pg. 273)

might not be local exceptions [see: local entropy decrease] to the general increase of entropy. For instance, regarded from the purely physical point of view, gold is a fairly ordinary metal; natural laws shew it no favor nor special treatment. Yet our visitor might notice that the world's total supply of gold, which had originally been fairly uniformly scattered throughout parts of the earth's crust, tended to become highly concentrated in a few small regions, in a way which would seem to set the demands of the second law of thermo-dynamics utterly at defiance. Again, the law does not approve of fires occurring at all, although it admits that accidents will happen [?]. It insists, however, that these accidental violations are most likely to occur when the weather is hot and dry. Yet our observer would not only detect innumerable fires on earth, but would notice that they occurred most frequently when it was cold and damp; he would see more in those parts of the surface of the earth which were covered with winter snow than in those which were parched with equatorial or summer heat. On the other hand, he might notice that small accumulations of ice were especially in evidence when the weather was hot and sultry.

The odds against all these events occurring in the normal course of a nature which had not been tampered with would be of the same order as the odds against a kettle of water freezing when placed on a hot fire. Thus, no picture of nature can claim to be complete, unless it contains some means by which the statistical laws of nature [?] may be evaded — if not throughout the whole of nature, at least in chosen spots on our own earth. Our visitor might perhaps conjecturally attribute these evasions to the activities of innumerable sorting demons.

(pg. 274)

A statistical survey of the more violent offences committed against the second law of thermodynamics would shew that the hotbeds of crime are precisely those places we describe as centers of civilization. Inanimate matter obeys the law implicitly; what we describe as life succeeds in evading it in varying degrees. In fact, it would seem reasonable to define life as being characterized by a capacity for evading this law. It probably cannot evade the laws of atomic physics, which are believed to apply as much to the atoms of a brain as to the atoms of a brick, but it seems able to evade the statistical laws of probability. The higher the type of life, the greater is its capacity for evasion. And the observed evasions so closely resemble the results that would be produced by an army of sorting demons, that it would seem permissible to conjecture that life operates in some similar way.

So long as nature was believed to be mechanistic, and therefore deterministic, such a conjecture was hardly permissible — the sorting demons would have interfered with the predestined course of nature.

On the other hand, modern physics can adduce no such objection to the conjecture; the only determinism of which it is at all sure is of a merely statistical kind. We still see the actions of vast crowds of molecules or particles conforming to determinism — this is of course the determinism we observe in our everyday life, the basis of the so-called law of the uniformity of nature. But no determinism has so far been discovered in the motions of the separate individuals; on the contrary, the phenomena of radioactivity and radiation rather suggests that these do not move as they are pushed and pulled by inexorable forces; so long as we picture them in time and space, their

(pg. 275)

future appears to be undetermined and uncertain at every step. They may go one way or another if nothing intervenes to direct their paths; they are not controlled by predetermined forces, but only by the statistical laws of probability. If an unknown something intervenes to guide them, they may transfer their allegiance from the laws of probability to the guiding something, as the molecules of the oil-water mixture did to the force of gravitation. There seems no longer to be any reason why this something should not be similar to the action of sorting demons, the volitions of intelligent minds loading the dice in their own favor, and so influencing, so to speak, the motions of the molecules when they are in doubt which path to take — provided always that volitions and molecules are not too dissimilar in their nature for such interaction to be possible.

§§: Space-time and Nature

We can also look at the matter in the alternative way described on p. 257. We have just been picturing nature as an assemblage of particles set in a framework of space and time. Yet we have seen elsewhere that such a framework is not suited for the arrangement of the whole external world, but only for the photons by which it sends messages to our senses. Because these messages arrive in a framework of space-time, we must not conclude that the whole external world exists within the confines of the same framework. Our observational knowledge of the outer world is limited by the aperture of our senses, and these form blinkers which prevent our seeing beyond space and time — just as our telescope may prevent us seeing more than a small angle of the sky. But the events we see

(pg. 276)

The rest of the chapter and book, in short, makes a passing attempt to argue for free will.

On 20 Jan 1934, Frederick Donnan, then auto-stylized as professor of physical and inorganic chemistry at University College, London, in a letter titled “Activities of Life and the Second Law of Thermodynamics” to Nature, gave a critical review of Jeans’ statement that life evades the second law; which reads as follows: [2]

“In The New Background of Science, Sir James Jeans, in discussing the activities of life in relation to the second law of thermodynamics, states that living organisms must possess some method of evading this law. He points out, for example, that a visitor to this planet from some tither universe would observe various curious and highly improbable arrangements of matter, such as collections of gold in various places [e.g. gold rings], numerous collections of ice in hot climates [e.g. ice cube in refrigerators], etc. These improbable arrangements or organizations imply presumably a decrease of entropy, that is, a violation of the second law. Surely, however, these actions are functionally inter-related with other simultaneous actions; namely, the metabolism and oxidation of food by the human organisms and the oxidation of fuel in such engines as they employ, and these causally inter-related actions involve an increase of randomness, that is, disorganization and consequent increase of entropy. I presume that Sir James Jeans would agree that the total effect will be a net increase of entropy.

An essential feature of the second law is that finite amount of organization may be purchased at the expense of a greater amount of disorganization in a series of inter-related spontaneous actions. If for a single moment the blood sugar circulating through the brains of Sir James Jeans' humans should cease to be oxidized, they would fall down unconscious and cease to be able to collect gold or ice. Is it good logic to pick out a series of actions which imply an increase of organization and there­fore a decrease of entropy, whilst neglecting simul­taneous interlocked actions in the same system which involve a greater increase of entropy; and then to announce as a mysterious result that the former actions evade the second law? Could one not reason in a similar manner that a crystal evades the second law when we watch a crystal growing in a supersaturated solution? No doubt the growth of the crystal involves per se an increase of organization, but this increase is purchased at the expense of a greater decrease of organization in the inter-related actions, as may very readily be demonstrated. Such examples in inorganic nature can be multiplied almost ad infinitum.

I do not wish to assume the role of a die-hard ‘defender of the faith’ (fidei defensor) of the science of the nineteenth century, or to assert or even suggest that the present known principles of science suffice to offer an adequate description of the phenomena of life. Indeed, in various publications I have striven to show that such an opinion or assertion would be quite un­justified. Nevertheless, I would humbly suggest that eminent physicists must not ignore the known and relevant facts of biochemistry, and that a knowledge of these facts may serve to remove a certain amount of mystery from their minds.”

On 3 Feb 1934, James Jeans, in his response letter, contended that a man who drives a railroad or a ship, such as the 68,000 horsepower Mauretana, above, can "decrease" the entropy of the world enormously, without any concordant significant "increase" in entropy, and that this is an example of subverting the second law.
On 3 Feb 1934, Jeans, in a response letter, titled “Activities of Life and the Second Law of Thermodynamics”, to Nature, responded to Donnan, as follows: [3]

“I am very glad to have elicited Prof. F. G. Donnan's critical views (Nature, Jan. 20, p. 99) on my suggestion as to life and thermodynamics, but confess I remain unconvinced by his arguments.

Prof. Dorman challenges my neglect of the body metabolism or fuel oxidation which, as he says, necessarily accompanies the arrangement or disarrangement of material objects by human activities, considering that such chemical changes may produce an increase of entropy sufficient to offset any [entropy] decrease produced by human intelligence. No doubt it may, but I cannot see that these two effects are ‘functionally interrelated’ or in any way suitable subjects for comparison. Given perfectly level and frictionless railways, a man may move millions of tons of matter, and thereby decrease the entropy of the world enormously, without incurring any corresponding increase of entropy through the combustion of food or fuel. Any increase of entropy which occurs in practice is a mere side-issue, an accident resulting from the impossibility of realizing ideal conditions, and so should not enter into the theoretical discussion at all.

A further increase of entropy might of course occur if the mental effort of arranging objects caused an increase in bodily metabolism. I believe orthodox physiology teaches that any such effect is inappreciable, but it is in any case obvious that it cannot be relied on to offset the decrease of entropy resulting from intelligent arrangement. We cannot, for example, suppose that the man who steers the Mauretania (Ѻ) consumes food-energy at a rate comparable with 100,000 h.p. more than normal, merely because he is guiding a ship of that horsepower. Prof. Donnan's parallel from crystal growth seems to me to fail through identifying ‘increase of organization’ with ‘decrease of entropy’. The two are equivalent so long as potential energy is unimportant, but when this becomes preponderating, as in a crystal, maximum entropy may well demand regular packing, and so maximum, not minimum, organization.”

Donnan | Guggenheim
On 15 Mar 1934 (published 7 Apr 1934 in Nature), Donnan teamed up with Edward Guggenheim, in opposition to Jeans, with a jointly-written rebuttal letter, which reads as follows: [4]

“In a recent letter [3] in Nature Sir James Jeans, in replying to a criticism made by one of us [2], writes: ‘Given perfectly level and frictionless railways, a man may move millions of tons of matter, and thereby decrease the entropy of the world enormously, without incurring any corresponding increase of entropy through the combustion of food or fuel’. Not only can this surprising statement be disproved, but the very reverse of it can be readily demonstrated. The entropy decrease associated with the sorting out of trucks depends not on the number of tons but on the number of trucks. Its magnitude would be the same if the trucks were replaced by an equal number of miniature trucks or counters or molecules. If a man were to sort out a million trucks, the entropy decrease would be of the same order of magnitude (to within a few powers of ten) as the increase of entropy when he breathes a million molecules of oxygen. To complete the proof of our assertion it is only necessary to estimate roughly how long it would take a man to sort out a million trucks and then estimate how many millions of millions of millions of millions of molecules of oxygen he must have breathed while he was doing it.

The same letter contains the statement: ‘We cannot, for example, suppose that the man who steers the Mauretania consumes food energy at a rate comparable with 100,000 h.p. more than normal’. Indeed, no one with a knowledge of thermodynamics would suppose so. The entropy associated with the steering of the Mauretania is of the order of magnitude of Boltzmann's constant k, simply because there is only one Mauretania being steered. In thermodynamic parlance, the difference between the total energy and the free energy associated with the motion of the centre of mass of the Mauretania is of the order of magnitude kT, where T is the absolute temperature, and this quantity is some 10^30 times smaller than the kinetic energy of the ship. The same thing may be expressed by saying that the Brownian movement of the Mauretania is negligible in comparison with its directed motion. In view of Sir James's lapse in thermodynamic reasoning, we consider it not unreasonable to challenge his vague reference to ‘orthodox physiology’, and ask on what experimental evidence he relies for his statement concerning entropy changes in the brain.”

On 21 Apr 1934, Jeans, responded as follows: [10]

“I am anxious to treat Prof. Donnan's views with all courtesy, but think his last letter, written in conjunction with Prof. Guggenheim, is entirely invalidated, like his previous letter, by a technical error in thermodynamics. The ordinary formula for the positional entropy of a large number of particles is:

k ∫∫∫ ν log ν dxdydz

where v is the number of particles per unit volume. Thus, moving N particles from a place of density ν to one of higher density ν' decreases the entropy by

kN (log ν’ – log ν)

Surely Profs. Donnan and Guggenheim have over­looked the factor N. Owing to its presence, moving a single molecule does not, as they contend, have the same effect as moving a truckload of N molecules, but only 1/Nth of this effect. The same error, I think, invalidates their second paragraph.

It is difficult to discuss views based on arguments which seem to me so entirely fallacious, so I can only repeat that I think the writers are in error by more than mere technical mistakes. They seem to me to be comparing two things that do not enter into relation with one another at all—like the number of calories in a man's dinner, and the number of ergs needed to carry it in from the kitchen to the dining-room.

As they ask for a physiological reference, may I (although no physiologist) refer them to F.G. Benedict and C.G. Benedict’s 1933 “Mental Effort in Relations to Gaseous Exchange, Heart Rate, and Mechanics of Respiration [N4].”

On 9 Jun 1934, Donnan and Guggenheim, in their response letter “Activities of Life and the Second Law of Thermodynamics”, stated the following: [9]

“We regret the necessity of prolonging this discussion, but in spite of the letter of Sir James Jeans [Nature, 133:612, Apr 21] we persist in the conviction that it is his reasoning, not ours, which is fallacious. We are quite aware that the change of positional entropy associated with the type of process which he cites involves the factor Nk, where k is the Boltzmann constant and N the number of particles concerned in the process, nor do we dispute the correctness of the well-known formula which he quotes. We must, however, point out that he is wrong in assuming that the number of ‘particles’ must coincide with the number of molecules. We might ask, why not the number of atoms, or the number of protons and electrons? The answer is, that for a given process of redistribution the particles are those units whose relationship to one another is altered but whose internal structure remains unaffected. In the process of sorting out trucks each truck is to be reckoned as a particle; in the process of steering the Mauretania the ship is a ‘particle.’

To revert to the type of case originally considered by Sir James Jeans, let us imagine a large number of equal spheres of glass on a frictionless horizontal plane. If N of these spheres be moved from a place where the (superficial) density of distribution of the spheres is ν to a place of higher density ν1, then the decrease–of positional entropy of the system is equal to kN (log ν 1 – log ν). According to Sir James Jeans, however, the decrease of positional entropy would be kn1 N (log ν 1 – log ν), where n1 is the number of molecules contained in each sphere. If he reasons in this manner, we would ask him why the decrease of positional entropy should not also be kn2N (log ν 1 – log ν), where n2, is the number of atoms, or the number of protons and electrons, contained in each sphere. This paradox clearly reveals the fallacy in his reasoning.

Finally, we would point out that the total entropy of an assembly of N identical systems, each made up of n ultimate particles, may be resolved into the sum of two terms, the first of the order Nk determined by the configuration (and relative motion) of the centers of mass of the N systems, the second of the order N(n – 1)k determined by the internal arrangement of the ultimate particles in each system. In any process in which the internal arrangement of the systems remains unchanged, only the first in the entropy is affected. We think it scarcely possible that Sir James Jeans would dispute this statement, although the views expressed in his last letter contradict it.”

On 30 Jun 1934, Jeans responded as follows: [11]

“I am at one with Profs. Donnan and Guggenheim in hoping that this discussion will end soon, but ask leave to explain why I think that their supposed paradox [N5] is merely a third mare's nest. It is a well-known, and indeed obvious, fact that entropy has different values according as it is measured with reference to atoms or molecules or other units. Profs. Donnan and Guggenheim have re-discovered this, hail it as a paradox, and claim that because this paradox exists my arguments must be unsound. As well might they rediscover the 'paradox' that temperature has different values according as it is measured on the Centigrade and Fahrenheit scale, and try to use this as ammunition against anyone who mentions temperature.”

On 18 Aug 1934, Donnan and Guggenheim published the following final statement of the debate: [8]

“In his last letter [N1], Sir James Jeans writes: ‘It is a well-known, and indeed obvious, fact that entropy has different values according as it is measured with reference to atoms or molecules or other units?’ If by entropy he means the absolute entropy of a given state of a system, his remark, though true, has no bearing whatever on the point at issue. If, on the other hand, ho means the entropy change in some definite process, such as the sorting out of trucks, then we suggest that he is unique amongst physicists in holding this opinion.

We have consistently maintained [N1], and still maintain, that the entropy change associated with the sorting of trucks is of the order of magnitude (to within a few powers of ten) Nk„ where k is Boltzmann's constant and N is the number of trucks sorted. Sir James Jeans, on the other hand, recently expressed the opinion [N3] that N should denote the number of molecules in the trucks. He now apparently suggests that it is merely a question of convention. Though we have discussed the matter with several authorities, including one of the most eminent theoretical physicists of the world, we have failed to find anyone, other than Sir James Jeans, who disagrees with us. We are content, therefore, to leave the matter in dispute to the judgment of the readers of Nature.”

Though we have discussed the matter with several authorities, including one of the most eminent theoretical physicists of the world, we have failed to find anyone, other than Sir James Jeans, who disagrees with us. We are content, therefore, to leave the matter in dispute to the judgment of the readers of Nature.”


In 1971, Nicholas Georgescu-Roegen, in his confused book The Entropy Law and the Economic Process, cited Jeans view as a violation of the second law view, stating that “the thought that life may be characterized by a capacity for evading this law [as professed by Jeans], once generally denounced as sheer obscurantism, is now endorsed by almost every authority in physico-chemistry.” [6]

The following are related quotes:

“In a fascinating interchange, Frederick Donnan and Edward Guggenheim argue against an assertion by the eminent physicist James Jeans, that life could yield a net increase in organization and therefore a decrease in entropy (Donnen 1934; Guggenheim 1934; Jeans 1934; called to my attention by Max Delbruck). In 1933, Jeans had written that ‘in fact, it would seem reasonable to define life as being characterized by a capacity for evading this law. It probably cannot evade the law of atomic physics, which are believed to apply as much to the atoms of a brain as to the atoms of a brick, but it seems able to evade the statistical laws of probability. The higher the type of life, the greater is its capacity for evasion’ (1933).”
Richard Adams (1988), The Eight Day (pg. 34) [5]

“A particularly remarkable exchange between Sir James Jeans and the physical chemist F. G. Donnan attests to the confusion. In four rounds of increasingly technical letters published in Nature in 1934, Jeans and Donnan insist on opposite answers to the question of whether the total (global) entropy production of metabolic processes—the organism in interaction with its environment—need be positive (Jeans claims no, Donnan yes). The debate itself produces a great deal of heat but ends where it begins, with Jeans expressing the hope ‘that this discussion will end soon’, and Donnan attempting to recruit allies sufficiently numerous to counteract Jeans' otherwise indisputable authority.”
— Evelyn Keller (1995), Refiguring Life [7]

“Typical views in the 1930's on this subject were expressed in an exchange of letters to the journal Nature between F. G. Donnan, a professor of physical and inorganic chemistry, and the physicist James Jeans. Donnan [1934] challenged the view expressed by Jeans in his book The New Background of Science that organisms must have some means for evading the second law of thermodynamics. Jeans [1934] replied that a person steering a large steamship adds little entropy in the activities of steering, but the ‘positional entropy’ of the cargo is changed considerably. This is due to moving the cargo from a location where it has a high density υ1 to a location where it has a low density υ2, thereby changing the positional entropy by ΔS = kBN[ln υ1 – ln υ2]. In this case, the intervention of an intelligent being is incidental to the entropy calculation. In spite of the entry of the physicist E. A. Guggenheim on Donnan's side, and the exchange of several more letters, this controversy died without being resolved and without, apparently, leaving any further trace. Jeans' positional entropy is only one example of the types of entropy proposed during this period.”
— Paul McEvoy (2002), Classical Theory (pg. 175)

See also
What is entropy debate | 1897-1907
● What is life in terms of physics and chemistry debate | 1946 (see: Bridgman paradox)
Rossini debate | 2007
Morarity-Thims debate | 2009

N1. Nature, 133, 986, Jun 30 1934.
N2. Nature, 133, 530, Apr 7, 1934. 133, 869, Jun 9, 1934.
N3. Nature, 133, 612, Apr 21, 1934.
N4. Benedict, F.G. and Benedict, C.G. (1933). “Mental Effort in Relations to Gaseous Exchange, Heart Rate, and Mechanics of Respiration” (abs), Washington: Carnegie Institution, No. 446:83.
N5. Nature, 133:869, Jun 9.

1. Jeans, James. (1933). The New Background of Science (§8: Events, pgs. 261-307; §§: Entropy, pgs. 269-78; quote pg. 280) (pdf). CUP Archive.
2. Donnan, Frederick. (1934). “Letter | Activities of Life and the Second Law of Thermodynamics” (Ѻ) (abs), Nature, Jan 20, 133:99.
3. Jeans, James. (1934). “Letter | Activities of Life and the Second Law of Thermodynamics” (abs), Nature, Feb 3, 133:174
4. Donnan, Frederick and Guggenheim, Edward. (1934). “Letter | Activities of Life and the Second Law of Thermodynamics” (abs), Nature, Apr 7, 133:530.
5. (a) Jeans, James. (1933). The New Background of Science. Cambridge University Press.
(b) Jeans, James. (1934). “Letter | Activities of Life and the Second Law of Thermodynamics” (abs), Nature, Feb 3, 133:174; also: Apr 21, Jun 30, Vol 133, pgs. 612, 986.
(c) Donnen, Frederick. (1934). “Letters”, Nature, Jan 20, Apr 7, Jun 9, Aug 18, Vol 133, pgs. 99, 530, 869; vol. 134, pg. 255.
(d) Guggenheim, Eduard. (1934). “Letters”, Nature, Apr 7, Jun 9, Aug 18, Vol. 133, pgs. 530, 869; Vol 134, pg. 255.
6. Georgescu-Roegen, Nicholas. (1971). The Entropy Law and the Economic Process (pg. 11). Cambridge, Massachusetts: Harvard University Press.
7. Keller, Evelyn. (1995). Refiguring Life: Metaphors of Twentieth-century Biology (pg. 62). Columbia University Press.
8. Donnan, Frederick. (1934). “Letter | Activities of Life and the Second Law of Thermodynamics” (abs), Nature, 134:255, Aug 18.
9. Donnan, Frederick and Guggenheim, Edward. (1934). “Letter | Activities of Life and the Second Law of Thermo-dynamics” (abs), Nature, Jun 9, 133:869.
10. Jeans, James. (1934). “Letter | Activities of Life and the Second Law of Thermodynamics” (abs), Nature, Apr 21, 133:612.
11. Jeans, James. (1934). “Letter | Activities of Life and the Second Law of Thermodynamics” (abs), Nature, Jun 30, 133:986.

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