I have read COUNTLESS explanations, countless examples, countless ELI5s. But I still have no fucking idea what entropy is. I’m **not** leaving this earth before I understand what it is. Thank you.
In: Physics
Consider a system that contains four particles. They each have two states, let’s call them high energy and low energy. We’ll represent this with 0 for low and 1 for high if you want. What are the possible states?
* 0000
* 0001
* 0010
* 0011
* 0100
* 0101
* 0110
* 0111
* 1000
* 1001
* 1010
* 1011
* 1100
* 1101
* 1110
* 1111
So with four particles, and two options each, we have 16 possible states. One thing you can immediately notice, the ordered states are rare. There’s just 0000 and 1111. 2 of 16.
So what is entropy? Literally that. It’s how many possible states there are, and how rare a given one is among them. The 0000 is low entropy. One like 1010 is just as rare, but it has many similar looking ones that together are high entropy. Just replace these the digits with atoms, and the two possible states with much more degrees of freedoms.
If you have a few billion, billion, billion atoms, there’s a lot of ways you could arrange them. A perfect crystal has a few options, but not many. An imperfect solid has a lot more options. A hot gas has way, way, way more options. So there’s just more ways to arrange a bunch of atoms that macroscopically look like a hot gas than there is that macroscopically looks like a perfect crystal. Just as an ordered number like 11111111 is rarer than a messy one like 10111010 if you were to randomly draw the numbers from a hat. And this is why entropy increases. If something changes, it’s way, way more likely to go to a messy state than an ordered one. It’s not impossible, but highly, highly unlikely.
Now you may be saying, my example looks an awful lot like binary numbers. And it is. Entropy and information are really the same thing. Ordering of states. You can measure entropy in bits. But the information we use on a computer is more abstract and of a much, much, much lower scale than the thermodynamic entropy of matter. Better to use J/K, the thermodynamic unit. Now, you may think that looks like some sort of relationship between energy (Joules) and temperature (Kelvin). But let’s roll this back for a second, and consider that temperature is actually the relationship, not entropy. Rather than entropy = energy/temperature. Consider that temperature = energy / entropy. Temperature is a relationship between changes in entropy with changes in energy. How does adding more energy change the possible states. That is temperature.
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