Schrödinger's Kitten

Irreverent Science for Everyone

Thursday 07 October 2010

Entropy, and the Lengths I Will Go To In Order To Justify My Squalor

  • macro
  • heat
  • universe

Entropy, or 'the measure of disorder in a system' (classic definition), is one of those nagging concepts, like quantum weirdness, that are easy to explain glibly, hard to grok, and seem to be fundamental to science as we know it and as we hope to know it better the following morning, slightly sweaty and with tousled hair and goofy grins. So it's a bit hubristic of me to invoke it to avoid tidying my room. But I do it anyway. This is why the second law of thermodynamics1 justifies my quite exceptional levels of messiness.

Heat Spreads

Thermodynamics covers the study of how heat moves, as might be reasonably expected from the name. So that covers conversion between different forms of energy, the work it does, the heat moving around, the temperature, pressure and volume changes, and generally the sorts of things that are very easily visualised and/or used to scald your hands.

This sort of stuff was big in the late 1700s and early 1800s when steam power was being worked on: lots of pistons, pumping, coke, and other exciting innuendo-laden things (if you need a refresher on this, check out The Men That Will Not Be Blamed For Nothing). The laws of thermodynamics describe how the energy something has relates to the work that has been done on it (squishing it, lifting it, stirring it) and the heat that's been put into it. There are four laws of thermodynamics, of which the undisputed master of disguise is the Second Law. It has a million different forms. Here are some:

  • It is impossible to build a heat engine that does nothing but convert heat into work — something will always be wasted
  • Heat does not spontaneously flow from cold objects to hot ones. You can build a refrigerator to move it, of course, but the operation of the refrigerator will heat up the world outside it more than it cools down the things within it.
  • If two objects are in contact and at different temperatures, they will equalize to the same temperature, and stay that way. You'll never catch them going back the other way.

In general: everything we do gives off heat, and heat spreads out and makes things more homogenous. There's no way of getting round it — as time goes on, energy is lost as heat which dissipates out to the surroundings. This 'lost', unusable energy is known as entropy. It can be quantified by dividing the exchanged heat by the temperature to get a comforting numerical measurement.

Disorder; Disorder; Disooooooorder!

On an atomic level though, heat is just how atoms move. Faster movement = hotter. So when we say heat is spreading out, we can also say that atoms are exchanging energy and tending to move at the same speed. Becoming more egalitarian and indistinguishable.2 This leads on to the second use of the concept of entropy, which is much more intangible and therefore appeals to Creationists, stoners who are convinced they've discovered the secret to the universe through hallucinogens, Discordians3, and other woolly thinkers.

In this context entropy is all about ordering. Consider doling out a certain amount of energy among 20 particles. If you give all the energy to one of them, leaving the rest with nothing, there are twenty ways to do this, one for each particle. If you give half of the energy to one particle and the remaining amount to another (assuming the energy and the particles are distinguishable close up), there are 380 ways to do it. Splitting the energy 10 ways gives you 670 billion (approx) ways to choose from, but the full 20-way split offers the most options at a massive 2.5 billion billion (approx) choices.4

This is just one example, but trust me, it's true all over — the more homogenous and mixed up a situation is, the more ways there are for it to happen. If each of these ways are equally likely to happen, the result is that it is more likely for things to be fairly, evenly distributed. Maybe this sounds like a pretty ordered result; but from a scientific point of view, order is about being able to distinguish individual elements. A featureless soup is about as disordered as you can get. And coincidentally, that's pretty much what my room looks like: a desk and a bed rising like oversized croutons from the consomme of books, shoes, clothes, art materials, cuddly toys, tools, and assorted frippery.

This gives another way to state the second law of thermodynamics, in terms of organisation — disordered states are more likely than ordered ones, and as more likely things happen more often, things tend to get more disordered with time. In fact, left alone, things tend towards disorder and it takes effort to bring them back.

With No Organisation, Nothing Gets Done

While some people love order very much5, in a thermodynamic context it results in nothing ever happening. All across the universe, changes are caused by uneven distribution of energy. Rocks fall because lifting them up involves giving them energy, and when support is removed they drop back to their low energy resting place on the ground. Hydrogen atoms fuse into helium inside the sun because a helium atom has less energy than the four hydrogen atoms that make it. When there is no inequality and energy is all fairly distributed, nothing happens, and this is what the universe is slowly, inexorably moving towards: slumping in the lowest energy state and doing nothing much.

But in the meantime, things do happen. Certainly the most inescapable example of this is life itself. For life to emerge, piles of amorphous molecules need to become lined up and spiral together in a dance of reproduction, spreading the (eventually fatal) condition of organisation. Not only does the existence of life create spatial order, it also needs to continue reducing entropy to live. Glucose molecules in food need to be reliably sorted out from the disordered mixture in the stomach, and passed on to gather in the places where they're needed. The entire business of an organism is taking in things it finds around and filing them in the almighty sorting-office of cellular processing. And this doesn't just apply to organic life either: to put anything in computer memory requires choosing a bit to be either 0 or 1, pinning it down to one value rather than the two possibilities before. If the data being recorded has a pattern, those 0s and 1s will violate entropy even harder.

The Unavoidable Side Effects Of Living

How does that gel with the second law of thermodynamics, then? The devil is in the details of its formulation: it only says that in an isolated system entropy will always increase. Otherwise you could disprove the second law by assembling a jigsaw. In real life, nothing is completely isolated, so the work done in ordering it will release energy to the surroundings, making everything slightly hotter and more entropic. This cancels out the gain in the order (and net cuteness) of the universe caused by reconstructing a picture of puppies in watering cans.

Creationists and other people who have decided not to burden themselves with the knowledge of exactly what they're arguing against often cite the second law of thermodynamics as a reason why life couldn't have spontaneously evolved. Leaving aside for the moment why they have respect for one bit of science more than another (surely that's cherry-picking? and surely their objection to cherry-picking is why they can't, like more sensibly minded Christians, regard Genesis as a myth, or at least a metaphor?), this would only apply if life existed in isolation. And oh momma, it does not.

Life Is Always Going To Get Messy

Like the jigsaw, life requires complicated and specific arrangements, and constantly creates them from chaos. That does reduce entropy. But to attain this order, energy is required, and some is bound to be lost to the surroundings. This heating generates much more entropy than the puny union of atoms in patterns takes away; and the books are balanced overall.

It is a feature of life that it is ordered, but an unavoidable side effect of order is that everything around has to become more disordered to compensate. I, your humble kitten, am a living being, and so I am a manifestation of order in the world6. Therefore my surroundings must work overtime at disorder to compensate, and avoid violating the second law of thermodynamics.

And that is why my room is messy; because I'm breathing.

You should be glad, mother.

1. Unfortunately not 'you do not talk about thermodynamics', else my second year physics marks would have been significantly better.

2. Yes, heat exchange is communist. That's why the hot tap is red.

3. I can say that, I'm a Discordian.

4. Where do these numbers come from? Permutations, ie the number of different ways you can choose x objects from a set of y and line them up. In this example, the distribution of energy amongst the particles (whether it's two ways, eight ways, or 16) is a 'macrostate'. It's a feature of the system that can be observed on a large scale. Each macrostate can arise through a number of different microstates (petty details — whether particle A gets the first twentieth of the energy, or particle B, etc). From the numbers I've given above, you can see that not all macrostates have the same number of microstates — in fact, there's a distinct bias towards the fairer ones. Since all microstates are equally likely, this means that fairer energy distributions are more likely. Much more likely. The more microstates a macrostate has, the more entropy it has. So more mixed up macrostates with more different arrangements possible within them — states with less order — have both more entropy and are more likely to happen.

5. I'm Chaotic Neutral, myself.

6. Despite my appearance.

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