Bad thermodynamics: Entropy
Usually my blog entries comment on some specific news item, but in other cases I’m motivated not by a particular current event or pseudoscience eruption, but by student questions or offhand comments I hear that demonstrate and remind me of some example of common bad thinking. One such example is the dramatically wrong way thermodynamics – specifically the concept of entropy – is often depicted in the popular media, in particular by opponents of evolution by natural selection.
Opponents of evolution are motivated by ignorance, and it shows. When they talk about thermodynamics and entropy, the supporters of creationism or “intelligent design” like to pretend they know something about the subject. This is really frustrating, as someone who has spent the better part of the last twenty years using thermodynamics to understand how rocks, water and bacteria interact with each other in nature. Thermo courses are almost universally feared by undergraduates and graduate students alike because of their difficulty. Even professional scientists who don’t devote sufficient attention and study can make profoundly basic mistakes when they talk about the topic. Like statistics, thermodynamics is difficult, complex, and should be used with care by the untrained.
Which is why I get frustrated at people who don’t understand entropy in the least, but have no qualms wielding it as a blunt instrument to attack evolution. Are these people equally insistent they know how to make their own antibiotics at home, or how to mine, refine and craft raw metals into household electronics, all by themselves? Do they do their own open-heart surgeries, too? I doubt it, and I doubt they’d claim such expertise… but when it comes to thermodynamics – and physics, for that matter – everyone feels entitled to their own loud, wrong opinions.
What is entropy, anyway? Stated simply, entropy is the measure of disorder in any system. Entropy can also be defined as a measure of the total amount of information in any system, but that definition can be confusing and so I’ll put it on the back burner for now. As a measure of disorder, entropy exactly quantifies how much of a jittery mess something is, relative to an imaginary state of textbook perfection and order.
A crystal is a lattice of atoms arranged in an exact, endlessly repeating matrix, where standing at one spot inside the lattice would be exactly like standing in a hall of perfect mirrors… infinite copies of yourself and the crystal scaffolding around you repeating forever in all directions, perfectly still and silent and majestic all the way out to the vanishing point. But few crystals even approach that Platonic ideal. Atoms inside crystals of quartz, or ice, or diamond are constantly jostling and vibrating. Some crystal atoms ping about like slow pinballs in a 3-D obstacle course, only coming to momentary rest when they encounter yawning caverns where structural elements of the crystal are missing. At a crystal’s surface lies not a smooth , infinite plain of pellucid clarity but a jagged topography as dramatic as Monument Valley… if Monument Valley were constantly shifting and warping, buttes rising, eroding, merging and dissolving as you watch. All of that imperfection, every crack or bouncing atom or shattered rift in a real-life crystal lattice is a taint of entropy. If someone could make a crystal that was perfect down to the atomic level, absolutely perfect inside and out, an avatar of Platonic ideality, and chilled to absolute zero… only then would it possess no entropy at all.
Perfect imaginary things at absolute zero possess zero entropy, but everything else – everything that actually exists in the real world – is entropically infected. Because we can reference entropy to an unreachable ideal state at absolute zero, entropy is an absolute quantity that varies with temperature. The farther something is from absolute zero – meaning the hotter something is – the higher its entropy value. Heat increases entropy, and cold decreases it.
When people say entropy is always increasing in the universe, well… they usually say that because they heard someone else say it and they think it sounds wise. Most people don’t know what they mean when they repeat this canard. But is it true? Is entropy always increasing in the universe? In short, yes… but only if you take the universe as a whole, and most of our questions about life and evolution don’t involve the universe as a whole, they involve little bits of the universe such as the Earth, or a dinosaur, or maybe an ice cube.
An ice cube is more ordered than the puddle of water it changes into in about ten minutes on your counter top. But what if you were to take that puddle of water and pour it (somehow) back into one cell of an ice tray, then put that ice tray outside in January in Michigan? If entropy is always increasing, that ice will forever remain molten water no matter what you do to it. If entropy is always making everything – literally, everything – more chaotic, then you could leave that little shot of water outside all night in a freezing blizzard and it would never freeze. In fact no water – anywhere – should ever refreeze once it melts, if the evolution-denialist’s version of entropy were true. But water does freeze, if the temperature drops below the freezing point of water. Why? Because entropy can decrease locally. The amount of disorder in a system can go down if energy is sucked away. The demands of entropy are such that the heat in a shot of liquid water can’t just remain inside the water if the world around it is a swirling blizzard of numbing cold. The meager amount of heat in a tiny glass of water will naturally spread itself out as widely as it can, just like a popped water balloon will spread its water all over your floor. Entropy demands that heat dissipates, and if one result is a local depression of disorganization in one little glass of water, then so be it. The pull of entropy on the heat in a glass of water is greater than the pull of entropy keeping its atoms chaotic. Nothing is violated. The laws of nature are served.
Local entropy losses happen all the time, all around us. Water vapor turns into highly ordered snowflakes. Magma turns into glittering quartz. Things like that happen because at room temperature quartz is more stable than a puddle of glowing silicic lava… in the lava puddle heat isn’t spread evenly relative to its environment. Once the heat spreads out the silica atoms lose sufficient energy to keep vibrating around, and so they settle down into a solid mass. If the lava is cooled slowly enough the atoms could even rearrange themselves back into an ordered quartz crystal. Why slow-cooled? Because otherwise the effect would be like a crowd of soldiers milling around in a barracks, when their drill sergeant bursts in and shouts “Atten-HUT!” The soldiers drop what they’re doing and stand up, wherever they are at the moment. The crowd freezes in whatever random arrangement of soldiers there happened to be just one moment prior to their sergeant yelling at them. If you take molten silica and instantly chill it to solidity, you’ll get glass: a disordered mass of chaotically arranged atoms standing still.
But why, if the lava were allowed to cool more slowly, and its atoms were allowed to rearrange themselves as the demands of heat flow and particle positioning dictate, would it order itself into a crystal at all? Imagine two people in an elevator. As strangers, the two people will stand apart from each other at two arbitrary places in the elevator car. Maybe one is standing next to the button panel, maybe the other is in the far corner talking on her cell phone. But what if a meeting upstairs lets out and fifteen people pile into the elevator with the original two, everyone riding down together on the way out of the building? It’s possible that ten of those people will squeeze tightly together in one corner, perhaps in some Boschian tangle of limbs and torsos that reaches to the ceiling, while the other seven stand around comfortably. That’s possible, but unlikely. What’s more likely is that the seventeen people will naturally put their arms to their sides to get skinnier, and jostle into a kind of ordered array of standing human bodies. They spontaneously order themselves, in other words.
Spontaneous generation of order is – paradoxically – one natural outcome of the cosmic demand for entropy. Entropy is like an invisible, intangible force that acts to even things out. In an elevator crowded with a Boschian tangle and a few comfortable passengers talking on their mobiles, entropy will tend to make the tangle even out… make the people shuffle around until everyone is as comfortable as they’re going to get until people start leaving the elevator. No one thinks about entropy in that case, it’s simply that every person tries to get comfortable, and the result is spontaneous organization… created by entropy. Confined inside a stifling elevator, people will each seek their lowest level of awkwardness… just as atoms in molten rock under pressure deep in the Earth’s crust will seek to minimize the total net forces acting on them by spontaneously snapping into an ordered crystal arrangement. No intent is involved, only force and response.
Spontaneous ordering is responsible for making crystals out of lava, ice out of water, queues out of throngs, and bubbles out of soap molecules. The latter example is exactly how we think the first cell membranes came together, by self-organization of organic molecules in water. Chemical reactions make order out of chaos all the time, and always by giving entropy its due. The recipe in DNA results in a transformation of food, water and air into a baby… at the cost of all the molecular disorder shed by the baby’s mother during gestation, including disorder from surrounding air being heated with body warmth, and disorder from structured organic matter (i.e. food) being turned into chaotic organic debris (i.e. urine and feces). A living creature is an island of order, collected and sorted via the actions of trillions of individual chemical reactions taking place all the time inside our cells and throughout our bodies. The difference in spontaneously-accumulated order between me and a crystal is one of magnitude, not of kind. But because the magnitude is so large it’s easy to lose perspective.
The entropy of the entire universe – taken as a whole – is certainly increasing, and will eventually (in something like 10 to the 100th power years) even out everything in the cosmos. When that happens no further interestingness can occur; no chemistry, no ice cubes, no life. But until then there will be lots and lots of places where knots of order can persist for a long time. Our Sun is one such knot, held together by a balancing act between gravity and explosive heat pressure… and for now entropy dictates that the Sun holds itself together. I should hope that entropy continues to allow islands of spontaneous order, otherwise the Sun, the Earth, you and I and everything else would instantly vaporize into a cold, thin mist of frozen atoms permeating an eternally silent universe.
So, race you to the pub?