The thermometer that probes the wort in my boiler nudges and flirts with 100°C. I turn on the tap. Earth-cold water races through a steel coil and coughs, splutters and then flows, hot and steaming, into the bathtub.
The thermometer begins to plummet, like a clock ticking down the moments to the end of things.
Time’s arrow is loose.
Of all the physical and chemical processes that are involved when I brew beer, cooling the wort resonates most with the fundamental nature of our universe.
I use a simple mechanism: a coil of stainless-steel tubing with cold water flowing through it, which sits inside the wort and sets off a heat exchange.
When I first used this mechanism, I was unsure whether the quickest results would come from passing the cold water through the coil fast or slow.
“Common sense suggests going slow,” I wrote. “The water being drawn off appears to be hotter the slower the flow, and, after all, that would seem to be heat that is no longer in the wort. The laws of physics suggest something else, however: the temperature of the entire coil should be kept as cold as possible to maximise the differential with the wort. A slow flow allows the water inside the latter part of the coil to reach a temperature that is too close to that of the wort.”
The laws of physics I was referring to are the laws of thermodynamics and, specifically, the second law of thermodynamics. This law states that the sum of entropies of interacting thermodynamic systems increases. The entropy of a system is the number of configurations or microstates that can be assumed by the components of that system, with a certain probability, given the defined macrostate of that system. In this case, the defined macrostates of our three systems, the wort and the coil and the rest of the universe, are their temperatures. The higher the temperature of a system, the more probable microstates it has and the higher its entropy is, because its constituent parts are moving around more.
The wort starts out hot, the coil starts out cold and the rest of the universe starts out super-cold. When I put the coil into the wort and they begin to interact, heat moves from the wort to the coil. This takes the wort-plus-coil system towards thermodynamic equilibrium, where the temperatures of the wort and the coil are the same. But, as the water rushes through the coil, it cools it enough to bring the wort-plus-coil system back away from thermodynamic equilibrium, and to set off the process of heat moving from the wort to the coil once more.
At first glance, this seems to violate the second law of thermodynamics. The temperature of the wort continues to fall, and therefore its entropy also decreases. But that’s only because we are ignoring the macrostate of our third system: the rest of the universe. The water that rushes out of the coil and into my bath is steaming hot. Imagine that steaming heat in the super-cold wastes of deep space: now you can understand how the decrease in entropy in the wort is more than offset by the increase in entropy of the coil-plus-the-rest-of-the-universe. Even when the wort has reached thermodynamic equilibrium with the water rushing into the coil, and “cold” tap water is running into my bath, that tap water has much more entropy than the empty depths of the universe.
In short, my wort cooling mechanism can get my wort down to 20°C in 20 minutes, but even if I were to run the tap to the end of eternity, the wort could never be as cold as the coldest part of the universe at this moment. Heat exchange must happen until equilibrium is attained.
We are always heading, not to a temperature of absolute zero and minimum entropy across the entire universal system, but to the point, just above absolute zero, of thermodynamic equilibrium and maximum entropy.
The macrostate of a system is a statement of the level of the dispersion and randomness of the components that make up its potential microstates. As such, it is a statement about the level of information that is available about its microstates. At a temperature of absolute zero, all of those constituents are tightly packed and unmoving, and we require no additional information beyond this macrostate of absolute zero to know the system’s microstate: the macrostate and microstate are identical—they are in the so-called “ground state”. Any rise in temperature is a move to a macrostate with more than one possible microstate: it represents a deletion of information, to be replaced by probabilities.
Is my wort cooler creating new information or destroying existing information?
At the local level, it appears to be creating new information in the wort. But it is only able to do that because the wort-and-coil is a non-isolated system: the information generated in (or the heat lost from) the wort is really just information lost from (or heat passed to) the rest of the universe.
The same is true of a refrigerator, or an air conditioner—or a human being. We are each of us a miraculous taming of the hot confusion of the Big Bang, and the fuming randomness of an exploding star. Our bodies and minds, as local systems, draw information out of this chaos. But our consumption, our metabolising, our sweating and shitting, our bodies and minds as they interact with the rest of the universe—it all hastens the march towards thermodynamic equilibrium, destroying information and returning us to the flat surface of pure randomness.
The organisation of a human being, like the think bubbles of beer foam, like the expanding universe, contains the elements of its own demise.
Is it all so hopeless, really?
A few weeks ago, my brother, who trained in high-energy particle physics, started talking to me about “Maxwell’s Demon”.
This is not a new idea. As the name suggests, it has its origins in a thought experiment formulated by James Clarke Maxwell in the mid-19th century. He imagined an isolated system of two gas-filled chambers resting in thermodynamic equilibrium and maximum entropy. Between the two chambers is a door. A demon stands at the door, opening and closing it to allow only fast-moving particles to move into chamber one and only slow-moving particles to move into chamber two. The result is an irreversible increase in the average temperature of the molecules in chamber one and an irreversible decrease in average temperature of the molecules in chamber two, and hence a decrease in entropy and an increase in information.
My wort chiller manages only to pull the wort-and-coil system away from thermodynamic equilibrium by the mechanism of allowing cold water to rush in and hot water to rush out—that is, it creates information locally only because it is non-isolated. Maxwell’s Demon, by contrast, appears to undo thermodynamic equilibrium and create information within an isolated system.
To my mind, Maxwell’s Demon is quite similar to a later thought experiment, formulated by the statistical physicist Marian Smoluchowski, called the “Brownian Ratchet”.
This mechanism consists of a ratchet and pawl connected to a paddle wheel that is immersed in a thermal bath of molecules undergoing Brownian motion. It is small enough that the collision of a single molecule can move the paddle wheel. Brownian motion is random, and would be equally likely to turn the paddle wheel clockwise or anti-clockwise. The ratchet and pawl only allow it to move in one direction, however—let’s say clockwise—and as a result this mechanism appears to generate work from the energy in the thermal bath without any movement of heat from one part of the system to another. By creating work out of randomness, information out of chaos, the Brownian Ratchet, like Maxwell’s Demon, appears to decrease the sum of the entropies of the constituent parts of its system.
Objections to this tend to appeal back to the second law of thermodynamics.
If the Brownian Ratchet is an isolated system with no heat gradient whose constituent parts are small enough to be moved by the impacts of single molecules, then the ratchet and pawl will undergo Brownian motion just as the molecules in the thermal bath do: if the pawl is bouncing around randomly then it cannot do its job of preventing the ratchet from turning anti-clockwise. The mechanism only works when the temperature of the ratchet and pawl is lower than that of the paddle wheel—but then what we have is a movement of heat from the paddle wheel to the ratchet and pawl, which is what creates the work and the emission of waste heat into the universe. This is no different from what I am up to with my wort-coil-universe system: the wort is the thermal bath and paddle wheel, the coil is the ratchet and pawl and the universe is, well, the cold, bleak, but not-quite-absolute-zero universe.
Maxwell’s Demon is similar to the pawl in the Brownian Ratchet. The pawl needs energy to stop the ratchet from moving anti-clockwise, and the Demon needs energy from the universe to gather information about the speed of the gas molecules in the two chambers he controls. The Demon’s increase in entropy will more than offset the decrease in entropy he affects by measuring the speed of the gas molecules, just as the increase in entropy of the coil-plus-the-rest-of-the-universe more than offsets the decrease in entropy in my wort.
That would appear to be that. These thought experiments merely serve to confirm the banal sovereignty of the second law of thermodynamics, the impossibility of perpetual motion machines, the unstoppable march towards the empty, echoing randomness of thermodynamic equilibrium.
Except that they are not merely thought experiments.
It turns out that nature is crammed full with Maxwell’s Demons and Brownian Ratchets—or at least, in attempting to figure out what’s going on in these natural machines, scientists have found the Brownian Ratchet to be the best model.
Moreover, in nature, those mechanisms are far, far more efficient at generating work with minimal heat loss than any machines that human beings have managed to create in their laboratories. Their local entropy-decreasing effects are more than offset by an increase in entropy in the universe—but the trade-off is infinitesimal, and those local effects are miraculously powerful.
Come to think of it, let me make a stronger statement.
These “molecular motors”, as they are known, are specifically protein structures that generate mechanical work from chemical fuel inside cells. Super-efficient Brownian Ratchets are not merely a feature of nature. They are a feature of life.
Thomas Aquinas, lecturing on Aristotle’s treatise on Physics, said something memorable about the nature of things. A thing’s nature, he argued, is an idea of a certain creative impulse within it, by which it moves to a determined end: “It is as if a ship maker were to bestow upon planks of wood the power to be moved, by themselves, into the form of a ship.”
Thomas didn’t know the half of it.
With molecular motors, nature appears to have bestowed upon parts of itself the power to be moved, by themselves, not merely into the form of a ship, but the form of a ship that can sail against nature’s own prevailing wind. The arrow of time takes us from the furious mix of information and randomness of the Big Bang to the flat randomness of thermodynamic equilibrium, but as long as that arrow is flowing there is still information in nature, fuel for the Brownian Ratchets of nature, unimagined by Thomas Aquinas.
The apparent telos of maximum entropy but minimum possibility might be overturned for an alternative telos of… what, exactly?
The tragedy of thermodynamic equilibrium is the tragedy of pure randomness with nothing or no-one to realise its potential as information. The last second of time will be the last chance to break the wave function of the entire universe, to maintain its being.
Against that tragedy I propose a comedy—perhaps a human comedy, perhaps divine. In that comedy, when the universe looks upon itself, it perceives that the beauty of its mix of order and disorder is precisely the beauty of being able to look upon itself. And it fights to maintain that disorderly order, the possibility of informed free will, of self-reflexiveness, dislodging the apparent telos of randomness with the true telos of intelligence.
It was always already the ship that knew how to build itself.
The thermometer that probes the wort in my boiler settles at 20°C. I turn off the tap. The water flowing from it is not much colder than that, now, and within seconds the water left in the coil settles into the dead embrace of equilibrium. Lost entropy sits steaming in my bathtub.
I’ve experienced the rare privilege of witnessing the end of a universe. But now, here I stand, the subject-creator, an Erlenmeyer flask of Saccharomyces cerevisiae in my omnipotent hands. This murky Milky Way of Maxwell’s Demons is ready to set off an equilibrium-shredding Big Bang.
And it’s going to be cosmic.
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