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Maxwell's Demon
Entropy, Information, Computing
By Harvey S Leff, Andrew F Rex PRINCETON UNIVERSITY PRESS
Copyright © 1990 IOP Publishing Ltd and individual contributors
All rights reserved.
ISBN: 978-0-691-08726-9
CHAPTER 1
Overview
Maxwell's demon ... [after J C Maxwell, its hypothecator]: 'A hypothetical being of intelligence but molecular order of size imagined to illustrate limitations of the second law of thermodynamics.' Webster's Third New International Dictionary
1.1 Introduction
Maxwell's demon lives on. After more than 120 years of uncertain life and at least two pronouncements of death, this fanciful character seems more vibrant than ever. As the dictionary entry above shows, Maxwell's demon is no more than a simple idea. Yet it has challenged some of the best scientific minds, and its extensive literature spans thermodynamics, statistical physics, information theory, cybernetics, the limits of computing, biological sciences and the history and philosophy of science.
Despite this remarkable scope and the demon's longevity, coverage in standard physics, chemistry and biology textbooks typically ranges from cursory to nil. Because its primary literature is scattered throughout research journals, semipopular books, monographs on information theory and a variety of specialty books, Maxwell's demon is somewhat familiar to many but well known only to very few. Two Scientific American articles on the demon (Ehrenberg 1967, Bennett 1987) have been helpful, but they only scratch the surface of the existing literature. The main purpose of this reprint collection is to place in one volume: (1) important original papers covering Maxwell's demon, (2) an overview of the demon's life and current status, and (3) an annotated bibliography that provides perspective on the demon plus a rich trail of citations for further study.
The life of Maxwell's demon can be viewed usefully in terms of three major phases. The first phase covers the period from its 'birth' in approximately 1867, through the first 62 years of its relatively quiet existence. The flavour of the early history is reflected in Thomson's classic paper on the dissipation of energy (Article 2.1). The second phase began in 1929 with an important paper by Leo Szilard (Article 3.1). The entry on Szilard in Scribner's Dictionary of Scientific Biography cites his '... famous paper of 1929, which established the connection between entropy and information, and foreshadowed modern cybernetic theory.' Notably, Szilard discovered the idea of a 'bit' of information, now central in computer science. His discovery seems to have been independent of earlier identifications of logarithmic forms for information by Nyquist (1924) and Hartley (1928). The term 'bit' (= binary digit) was suggested approximately 15 years after Szilard's work by John Tukey. The history of the demon during the first two phases is described by Daub (Article 2.2), Heimann (Article 2.3) and Klein (Article 2.4).
After a hiatus of about 20 years, Leon Brillouin (Article 2.5) became involved in the Maxwell's demon puzzle through his interest in finding a scientific framework in which to explain intelligent life. Subsequently Brillouin (Article 3.2) and Dennis Gabor (Article 3.6) extended Szilard's work, focusing on the demon's acquisition of information. Rothstein formulated fundamental information-theoretic interpretations of thermodynamics, measurement, and quantum theory (Article 2.6). Both Brillouin and Gabor assumed the use of light signals in the demon's attempt to defeat the second law of thermodynamics. The result was a proclaimed 'exorcism' of Maxwell's demon, based upon the edict that information acquisition is dissipative, making it impossible for a demon to violate the second law of thermodynamics.
In 1951, independently of Brillouin, Raymond published an account (Article 3.3) of a clever variant of Maxwell's demon that did not explicitly entail light signals—a 'well-informed heat engine' using density fluctuations in a gas. Raymond found that 'an outside observer creates in the system a negative information entropy equal to the negative entropy change involved in the operation of the engine.' His work, though less influential than Brillouin's, also made the important connection between information and entropy. Finfgeld and Machlup (Article 3.4) analyzed Raymond's model further, assuming that the necessary demon uses light signals, and also obtained an estimate of its power output.
The impact of Brillouin's and Szilard's work has been far-reaching, inspiring numerous subsequent investigations of Maxwell's demon. Clarifications and extensions of Brillouin's work by Rodd (Article 3.5) and Rex (Article 3.9) are reprinted here. Weinberg broadened the demon's realm to include 'macroscopic' and 'social' demons (Article 2.8). Despite some critical assessments (Articles 2.7, 3.7 and 3.8) of the connections between information and entropy, those linkages and applications to the Maxwell's demon puzzle remain firmly entrenched in the scientific literature and culture.
The third phase of the demon's life began at age 94 in 1961 when Rolf Landauer made the important discovery (Article 4.1) that memory erasure in computers feeds entropy to the environment. Landauer referred to Brillouin's argument that measurement requires a dissipation of order kT, and observed: 'The computing process ... is closely akin to a measurement.' He also noted that: '... the arguments dealing with the measurement process do not define measurement very well, and avoid the very essential question: When is a system A coupled to a system B performing a measurement? The mere fact that two physical systems are coupled does not in itself require dissipation.'
Landauer's work inspired Charles Bennett to investigate logically reversible computation, which led to Bennett's important 1973 demonstration (Article 4.2) that reversible computation, which avoids erasure of information, is possible in principle. The direct link between Landauer's and Bennett's work on computation and Maxwell's demon came in 1982 with Bennett's observation (Article 4.4) that a demon 'remembers' the information it obtains, much as a computer records data in its memory. Bennett argued that erasure of a demon's memory is the fundamental act that saves the second law. This was a surprising, remarkable event in the history of Maxwell's demon. Subsequent analyses of memory erasure for a quantum mechanical Szilard's model by Zurek (Article 4.5) and Lubkin (Article 4.7) support Bennett's finding.
A key point in Bennett's work is that, in general, the use of light signals for information acquisition can be avoided. That is, although such dissipative information gathering is sufficient to save the second law of thermodynamics, it is not necessary. Bennett's argument nullifies Brillouin's 'exorcism', which was so ardently believed by a generation of scientists. The association of the Maxwell's demon puzzle with computation greatly expanded the audience for the demon, and writings by Bennett (Articles 4.4 and 4.8), Landauer (Article 4.6), and Laing (Article 4.3) illustrating that association are reprinted here.
These three phases of the life of Maxwell's demon are described in further detail in Sections 1.2–1.5. Section 1.6 deals with aspects of the demon not treated in the earlier sections. Chapters 2–4 contain reprinted articles covering, respectively: historical and philosophical considerations; information acquisition; and information erasure and computing. This is followed by a chronological bibliography, with selected annotations and quotations that provide a colourful perspective on the substantial impacts of Maxwell's demon. An alphabetical bibliography plus an extensive index is also included.
1.2 The Demon and its Properties
1.2.1 Birth of the Demon
The demon was introduced to a public audience by James Clerk Maxwell in his 1871 book, Theory of Heat. It came near the book's end in a section called 'Limitation of The Second Law of Thermodynamics'. In one of the most heavily quoted passages in physics, Maxwell wrote:
Before I conclude, I wish to direct attention to an aspect of the molecular theory which deserves consideration.
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.
Maxwell's thought experiment dramatized the fact that the second law is a statistical principle that holds almost all the time for a system composed of many molecules. That is, there is a non-zero probability that anisotropic molecular transfers, similar to those accomplished by the demon, will occur if the hole is simply left open for a while.
Maxwell had introduced this idea in a 1867 letter to Peter Guthrie Tait (Knott 1911) '... to pick a hole' in the second law. There he specified more detail about the sorting strategy intended for the demon:
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.
This allows a molecule to pass from A to B if its kinetic energy is less than the average molecular kinetic energy in B. Passage from B to A is allowed only for molecules whose kinetic energies exceed the average kinetic energy/molecule in A. In the same letter Maxwell emphasized the quality of 'intelligence' possessed by the demon:
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.
William Thomson (1874, Article 2.1) subsequently nicknamed Maxwell's imaginary being 'Maxwell's intelligent demon'. He apparently did not envisage the creature as malicious: '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.' He expounded further on his view of 'the sorting demon of Maxwell' (Thomson 1879):
The word 'demon', which originally in Greek meant a supernatural being, has never been properly used to signify a real or ideal personification of malignity.
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.
'Dissipation of Energy' follows in nature from the fortuitous concourse of atoms. The lost motivity is essentially not restorable otherwise than by an agency dealing with individual atoms; and the mode of dealing with the atoms to restore motivity is essentially a process of assortment, sending this way all of one kind or class, that way all of another kind or class.
Following Thomson's introduction of the term 'demon', Maxwell clarified his view of the demon (quoted in Knott 1911) in an undated letter to Tait:
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.
4. Is the production of an inequality of temperature their only occupation? No, for less intelligent demons can produce a difference in pressure as well as temperature by merely allowing all particles going in one direction while stopping all those going the other way. This reduces the demon to a valve. As such value him. Call him no more a demon but a valve like that of the hydraulic ram, suppose.
In light of Maxwell's intentions, it is interesting to examine the accuracy of dictionary definitions. The Webster's Third New International Dictionary definition quoted at the beginning of this chapter, though brief, properly cites Maxwell's intention to 'illustrate limitations of the second law of thermodynamics.'
In contrast, The Random House Dictionary of the English Language (Second Edition 1988) contains the definition:
A hypothetical agent or device of arbitrarily small mass that is considered to admit or block selectively the passage of individual molecules from one compartment to another according to their speed, constituting a violation of the second law of thermodynamics.
And the second edition (1989) of The Oxford English Dictionary describes it in the entry for James Clerk Maxwell:
... a being imagined by Maxwell as allowing only fast-moving molecules to pass through a hole in one direction and only slow-moving ones in the other direction, so that if the hole is in a partition dividing a gas-filled vessel into two parts one side becomes warmer and the other cooler, in contradiction to the second law of thermodynamics.
Despite the emphasis on violating rather than illustrating limitations of the second law in these two definitions, there is no indication that Maxwell intended his hypothetical character to be a serious challenge to that law. Nevertheless, the latter two definitions reflect the interpretation by many subsequent researchers that Maxwell's demon was a puzzle that must be solved: If such a demon cannot defeat the second law, then why not? And if it can defeat the second law, then how does that affect that law's status?
Maxwell did not relate his mental construction to entropy. In fact, he evidently misunderstood the Clausius definition of entropy and went out of his way to adopt a different definition in early editions of his Theory of Heat. He wrote: 'Clausius has called the remainder of the energy, which cannot be converted into work, the Entropy of the system. We shall find it more convenient to adopt the suggestion of Professor Tait, and give the name of Entropy to the part which can be converted into mechanical work.' He then argued that entropy decreases during spontaneous processes. Later Maxwell recanted: 'In former editions of this book the meaning of the term Entropy, as introduced by Clausius, was erroneously stated to be that part of the energy which cannot be converted into work. The book then proceeded to use the term as equivalent to the available energy; thus introducing great confusion into the language of thermodynamics.'
(Continues...)
Excerpted from Maxwell's Demon by Harvey S Leff, Andrew F Rex. Copyright © 1990 IOP Publishing Ltd and individual contributors. Excerpted by permission of PRINCETON UNIVERSITY PRESS.
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