What is entropy?
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Entropy can be described in 2 ways. The first is how much of the energy in a system is unable to do work. If you take a log, it has potential energy. If you burn that log, you turn that potential energy into heat and light. We can use that to do work, like boil water, but after the fire goes out, all of that energy has been released, and the log may still be hot, but we can no longer boil water with it. No energy was destroyed, but we now have less energy that can do work.
The other way to describe it is disorder. If I have milk, and chocolate, I can make chocolate milk. If I put them together, I just have chocolate in milk, but I have to mix it up in order to make chocolate milk. Once the mixing is done, I can’t unmix the chocolate milk. All of the milk particles and chocolate particles are mixed up, and the system is disorganized.
Before the mixing, if I switched a chocolate particle and a milk particle, that’s a big change because now I have a piece of milk surrounded by chocolate, and a piece of chocolate surrounded by milk. After the mixing, switching a chocolate and a milk particle isn’t a big change because you go from a mix of chocolate and milk, to a nearly identical mix of chocolate and milk. I can’t mix up the chocolate milk any more, and it won’t spontaneously unmix itself.
Bridging the connection between those two descriptions of entropy is the key to understanding it. Mixing the chocolate milk is like getting the energy to do work. Once the chocolate milk is all mixed together, there’s no more work that energy can do, the chocolate milk doesn’t get any more mixed if we keep stirring and nothing we can do will unmix it.
Why does entropy always increase though? There’s no magical force that pushes entropy to increase, it’s just the result of statistics. If we want unmixed chocolate milk, there’s only 1 way to get it. All the chocolate on one side (we’ll call it the bottom) and all the milk on the other (top). If we want chocolate milk that’s mixed, there’s billions of ways to do it, we just need ro randomly place chocolate a milk particles. Randomly switching a chocolate and milk particle won’t affect how mixed up the chocolate milk is. If we let the system do its own thing (particles randomly bouncing around, which will happen for anything with temperature) then it’s far more likely to end up in one of those mixed states, than the one unmixed state.
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