Maxwell’s Demon: A Tale of Two Entropies (Part 1 of 2)
Even if you don’t know what it is, you have probably heard of “Maxwell’s Demon.”
Like Schrödinger’s Cat, Maxwell’s Demon circulates in the cultural imagination more potently than the actual thought experiment it originally signified. The brainchild of James Clerk Maxwell in 1867, what we call “Maxwell’s Demon” has survived more than a century of technological transitions and remains wedded to the concept of “entropy,” though what that means, exactly, is complicated and differs from its Victorian origins.
In this two-letter series, I will explore the birth and evolution of Maxwell’s Demon. Part 1 lays the historical, political, and conceptual groundwork for a subsequent discussion of what entropy means to basic Information Theory (Part 2). Depending on your background, or from where you’ve acquired familiarity with the term “entropy,” you might associate this word with one of two very different registers: on the one hand, entropy signals disorder, dissipation, and “heat death.” On the other hand, it also means information, “equivocation,” and the destruction of information as memory.
What feels like a tension between these groupings of definitions is really more like a point of rupture in cultural association, where a Victorian allegory (the demon) gets imported into the information age and is forced to fine-tune how he mediates between cultural anxiety (or desire) and physical theory. What is fascinating about Maxwell’s Demon, I think, isn’t as much what Maxwell’s original thought experiment was, or how that concept mutated to fit the twentieth century, but rather how allegory performs those operations across time.
So, what follows is a Tale of Two Entropies, and the story of how Maxwell’s Demon remains the hinge point of two different, yet generative, scientific applications.
Introducing Thermodynamic Entropy
Maxwell’s Demon is a thought experiment designed to reveal the statistical nature of the second law of thermodynamics. In order to understand what the demon does, we need to establish a basic understanding of this law, and the kind of cosmological resonance it had in the mid-nineteenth century.
The second law of thermodynamics (sometimes referred to as the “entropy law” or the “law of dissipation”) places a directionality constraint on energy transfers. It states that, in a closed system, the amount of work-available energy moves down a gradient from availability to diffuseness. This is why restoring a closed system to a higher state of order requires an outside input of energy; or, taking the universe as a closed system, this is why the universe naturally drifts towards a state of cold, workless equilibrium, or “heat death.” This is also why your coffee will not spontaneously reheat itself, and why perpetual motion machines (i.e., getting work output for nothing) cannot exist. The arrow of time is inextricable from such processes.
In 1865, Rudolf Clausius attached a new word to this dismal concept. He coined the term, “entropy,” to denote the energy unavailable for work production, a value which necessarily increases over time in any closed system. Clausius arrived at “entropy” partly because it sounded like “energy,” and partly because its roots include the Greek word for transformation [1]. For Clausius and his contemporaries, entropy was a measure of the disorder in a system.
One of those contemporaries was William Thomson (Lord Kelvin), who, like Clausius, published an interpretation of the two laws of thermodynamics. Thomson formally synthesized his own findings with those of James Prescott Joule, Clausius, and Macquorn Rankine; and, in 1852 Thomson presented a short series of papers to the Royal Society of Edinburgh that clarified what he called the “dissipation” of mechanical energy as a universal tendency in nature [2].
“Dissipation” was as much a mood as it was a state of matter. Thomson selected “dissipation” to describe the energetic tendency to drift towards diffuseness; but dissipation was also a common nineteenth century term used to modify subjects as wasteful, unproductive, morally depraved, or frittered out [3]. The world and its irreversible processes were getting less and less productive, Thomson argued. And it was up to man (read: the British) to direct each transfer of energy in the most useful, work-extractive manner possible.
Moreover, Thomson attached a cosmological, Judeo-Christian reading to the inevitability of universal heat death. In his 1862 lecture, “On the Age of the Sun’s Heat,” he weaponized the logic of thermodynamics against Charles Darwin and his secular colleagues by calculating (incorrectly, as it turned out) the age and fate of the sun. Thomson declared,
“It seems, therefore, on the whole most probable that the sun has not illuminated the earth for 100,000,000 years, and almost certain that he has not done so for 500,000,000 years. As for the future, we may say, with equal certainty, that inhabitants of the earth cannot continue to enjoy the light and heat essential to their life, for many million years longer, unless sources now unknown to us are prepared in the great storehouses of creation” [4].
By deploying thermodynamics to argue that the sun simply could not have been burning for as many years as Darwin claimed natural selection had been at work, Thomson threatened the then-nascent theory of evolution in an attempt to shore up evidence for the theory of Creation. His, again incorrect, calculations also generated an estimated death date for the sun. Such an end-days vision of entropy or dissipation brought a sense of material finality to traditional Christian cosmology. It certainly worked to shut the secular materialists up for a while, and it unsettled Darwin, in particular.
So, when James Clerk Maxwell introduced entropy as a statistical law, his thought experiment – “Maxwell’s Demon” – became the center of a thermodynamic controversy.
Maxwell Invents a “Being”; Thomson Creates a “Demon”
It’s not that Maxwell was opposed to Thomson’s theological agenda; and in fact Maxwell’s own Anglo-Scottish background perpetuated his tendencies to reify a Platonic sense of spiritual idealism in mathematical and physical law. However, Thomson and Maxwell happened to approach the entropy law from different perspectives.
Maxwell had been corresponding with Clausius for some time on the molecular behavior of gases. Specifically, where Clausius introduced several important and novel concepts to illustrate how the temperature of a gas can be described in terms of its energy, Maxwell raised the stakes of Clausius’s kinetic model by arguing that a statistical method must replace a strict dynamical method of calculating molecular motion [5].
This means that, because spontaneous fluctuations in the motions of individual molecules are always occurring, we can only ever talk about molecular averages. In the deep cold of space, for instance, there are individual molecules zooming about with heat energy. However, because the average molecular motion remains so tiny, those zooming outliers do not represent what we perceive. What this means for the second law of thermodynamics, more importantly, is that it has only statistical certainty, or that the law itself describes the properties of a system, but does not describe the properties of any individual molecule in that system.
Let’s think about what that means for Thomson’s elaborate, apocalyptic prescription for the end times. While defining entropy as a statistical law does not endanger its “truth” (the second law of thermodynamics has never been “in danger”), it does question the absoluteness of entropy. It certainly asks us to think about the finality of “heat death” differently. Even if we can’t extract work from the universe, or from any closed system, because it has reached thermodynamic equilibrium, we can only ever describe heat energy in terms of its macrostates. Maxwell insisted that it was impossible to go pointing at this or that molecule and report on its individual energy. Certainly some individual molecules are moving faster than their average macrostates. This fact doesn’t undo entropy, of course, but it confines the second law of thermodynamics to the realm of statistics. All this talk of being “statistically certain” dilutes the cosmic register of Thomson’s apocalyptic heat death.
Enter the demon.
In an 1867 letter to Peter Guthrie Tait, another British thermodynamicist, Maxwell illustrated his statistical argument with a thought experiment in which a “neat-fingered being” “knows the paths and velocities of all the molecules” in a chamber, but “can do no work except open and close a hole in the diaphragm by means of a slide without mass” [6]. In his 1871 Theory of Heat, he elaborated on this concept:
“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” [7].
The being monitors the microstates of a thermodynamic system and acts as an internal agent, vetting the pathways of molecules based on their respective energies. By preventing the entropic drift from a hotter to a colder state, the being can thus extract continuous work from such an engine. It operates as a perpetual motion machine, giving us work for nothing. Simply by observing the movements and ordering these molecules into different chambers, the being prevents thermodynamic equilibrium. Of course, there are no tiny beings with massless, frictionless doors; and so we don’t know the energy states of individual molecules. Entropy remains statistically reliable.
You may have noted that Maxwell did not call his being a “demon.” In 1879, Thomson delivered a lecture titled, “The Sorting Demon of Maxwell,” in which he described (and popularized) Maxwell’s molecule-sized homunculus in far greater detail than Maxwell ever did [8]. In fact, Maxwell rejected Thomson’s moniker for his being, urging his colleagues to think of it more as a valve than a demon [5].
But Thomson’s appropriation of the term, “demon,” is adequate, considering what “daemonic” figures do.
Bruce Clarke’s reading of scientific allegory offers up a neat definition: “Daemons are agents of communication, typically taking the shape of messengers, or guardians, or other figures of admonition. The crucial thing is that they can take whatever shape the larger conceptual scheme demands: they are inherently metamorphic.” The daemon operates by “bridging conceptual gaps and bearing important cultural information” [6].
The daemon balances abstract concepts, theories, and desires with concrete images or modeling. And, in the interstices of those physical phenomena and cultural desires, a concept – like entropy – can harden into something new. Indeed, this is exactly the function Maxwell’s Demon occupied in Victorian scientific culture. As an agent of communication, the demon performs a physical impossibility to undercut the theological absolutism of the entropy law, and, with it, the authority of William Thomson’s projection for the end of life on earth.
Clarke suggests that Maxwell’s Demon gestures to a “desire to secure conceptual salvation from the finality of that last judgment” [6]; yet, I wonder whether the being/daemon/demon wasn’t performing more of Maxwell’s desire to concretize the limitations of the second law of thermodynamics, particularly from the perspective of (human) beings less “clever” and “neat-fingered” than that of his thought experiment. Maxwell was not irreligious; he, like Thomson, maintained that only God could restore energetic order and prevent thermodynamic equilibrium. But by jettisoning the dynamical theory of gases, he also recognized that we can only ever calculate that entropic drift with statistical certainty.
The Demon Evolves
Despite Maxwell’s intention for his Demon, several of his colleagues did feel threatened by the implications of the thought experiment. They worked deliberately to tame the Demon back into Thomsonian cosmology.
In particular, Tait (the recipient of the letter where Maxwell originally described his Demon) and another scientist, Balfour Stewart, anonymously published a notorious volume called The Unseen Universe or Physical Speculations on a Future State (1875). Like most Victorian texts, The Unseen Universe belongs to the public domain and can be found here. If you have time, you really should explore this gem of whackadoodle logic. Think of it as you might Ancient Alien theory: a little bit of scientific popularizing, a whole lot of far-fetched speculation, and packed with politics about the authority of science.
The Unseen Universe was published in response to John Tyndall’s infamous “Belfast Address.” In the autumn of 1874, Tyndall delivered the address to the British Association for the Advancement of Science, arguing in favor of secular materialism. Tyndall argued that only science, not religion, offered a way to learning the “true” nature of phenomena [9]. It’s important to understand here that he was contributing to an ongoing debate on how to define the contours of the scientific establishment. That is, what counts as legitimate science? How should we (the British) define disciplinarity? Where should religion fit here, if at all?
As traditional Christian moralists, Stewart and Tait countered in The Unseen Universe that indeed the physical laws of science pointed to a real yet invisible spiritual reality [10]. They co-opted Maxwell’s Demon, turning it into an “army” of demons with many doors, operating against entropy seemingly at the command of a higher intelligence. By altering the narrative, the Demon becomes assimilated into Thomson’s apocalyptic entropy: in The Unseen Universe, we cannot escape entropy because, as Clarke puts it, “the fallen material constitution of the world is bound to foil any attempt we might make” [6].
It’s important to understand that this is different from Maxwell’s original interpretation. Maxwell never intended his “being” to offer the possibility of escape from the second law of thermodynamics. Yet the “many demons” narrative twists the Demon into a fallen hero who tries yet cannot outwit the Law of Nature.
Born in 1867, Maxwell’s “neat-fingered being” had already evolved by 1875. By the dawn of the information age, he would evolve much more. This is what we will explore in the second part of “A Tale of Two Entropies”: what Maxwell’s Demon did for Information Theory.
Citations
[1] Clausius, Rudolf. The Mechanical Theory of Heat, with Its Applications to the Steam-Engine, and to the Physical Properties of Bodies, edited by T. Archer Hirst, Introduction by John Tyndall, London: John Van Voorst. 1867.
[2] Thomson, William. “On a Universal Tendency in Nature to the Dissipation of Mechanical Energy,” in The Philosophical Magazine 4, 1852.
[3] “dissipated, adj”. OED Online. September 2020. Oxford University Press.
[4] Thomson, William. “On the Age of the Sun’s Heat.” Macmillan’s Magazine, March 1862, 388-93.
[5] Harman, P.M. Energy, Force, and Matter: The conceptual Development of Nineteenth-Century Physics. Cambridge University Press, 1982.
[6] Clarke, Bruce. Energy Forms: Allegory and Science in the Era of Classical Thermodynamics. University of Michigan Press, 2001.
[7] Maxwell, James Clerk. Theory of Heat. 1871. Ninth Edition. Longmans, Green and Co., 1888.
[8] Thomson, William. “The Sorting Demon of Maxwell.” Proceedings of the Royal Institution. Vol. ix, February 28, 1879. 113.
[9] Tyndall, John. Address Delivered Before the British Association Assembled at Belfast. Longmans, Green, and Co. 1874.
[10] Stewart, Balfour, and P.G. Tait. The Unseen Universe of Physical Speculations on a Future State. Macmillan, 1875.