What is Entropy?

The laws of thermodynamics teach us three things:

  1. Energy can neither be created, nor destroyed.
  2. Over time, entropy within a system tends to increase.
  3. As the amount of heat in a system approaches zero, the amount of entropy approaches a certain constant value.

The part that confuses people is the “entropy” part. People tend to think that entropy means disorder. One example I read, which was posted by a high-school science teacher, compared entropy to a messy room. If you don’t clean your room, it will get messier and messier, and eventually it will be really messy, and that’s maximum entropy.

Wrong, wrong, and wrong.

 

Let’s put it into terms a teacher can relate to, and consider the thermodynamics of an elementary school classroom.   Keep in mind, we aren’t talking about a box of steam anymore.  We are talking about a very important kind of system, which we call a “complex self-organizing system.”  Here goes:

  1. Kids have a lot of energy, but fortunately, any given classroom can only have so much energy in it. Thank God.
  2. Over time, kids tend to simmer down.
  3. Eventually, if the kids continue to simmer down, they will approach a state of order, in which every kid is in a seat, the desks are in neat rows, everyone is facing in the same direction, no one’s hair is messed up, and everyone is perfectly quiet.

 

Questions?

I can imagine a higher state of entropy than that. Supposed the kids fall asleep. That’s not very orderly, they will be sprawled all over everything.” A room full of sleeping children is not called a “classroom,” it is called “a slumber party.” A slumber party will reach a different state of entropy than a classroom. But there’s not a substantial difference. The point is, if the kids are running around the room screaming and yelling, any kid could be in any number of states at any given time. Sitting, running. Yelling. Crying. They could be anywhere in the room. In either the classroom or the slumber party, the kids are only in one state, and you know where each kid is at any given time. So both are good examples of entropy.

What’s this about self-organizing? No classroom organizes itself.” A roomful of children without a teacher present is not called “a classroom,” it’s called “Chuck-E-Cheese.” It doesn’t matter that you are the only one in the classroom that wants to see it organized; if you are in there organizing it, it’s a self-organizing system.

So entropy isn’t disorder?” No, it’s not. Systems tend to cool over time, meaning that energy leaks out of the system. As it cools, we see an inverse relationship between the amount of energy in the system and the amount of entropy in the system. As the energy level falls, entropy rises. It’s helpful to think of entropy as being like crystallization. So one way of expressing the third law is, things that can crystallize, will do so if the temperature gets low enough. Once they crystallize, the process is done; entropy doesn’t continue to increase.

This is critically important. Entropy is a pattern. It’s a special kind of pattern. It’s the pattern your system will settle into naturally. It settles into this pattern with minimal energy. If it takes energy to maintain the pattern, then you’re not talking about entropy any more. The pattern of entropy doesn’t require any energy at all. One way of expressing the second law is, “energy runs downhill.” If you get that, then understand that entropy is what the landscape looks like at the very bottom of the hill.

If you’re a teacher, you can arrange the desks in your room any way you want. Maybe you think a circle might work better. Or maybe you think an auditorium arrangement might work best. This is part of the art of being a teacher. Arrange the desks and the kids will find them.

Keep this concept in mind as we talk about thermodynamics in general, and the thermodynamics of complex self-organizing systems in particular.

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