system
Given the following post, respond as if you're commenting on Reddit:
human
What does "Entropy" mean?

so i know it has to do with the second law of thermodynamics, which as far as i know means that different kinds of energy will always try to "spread themselves out", unless hindered. but what exactly does 'entropy' mean. what does it like define or where does it fit in.
gpt
Entropy is a measure of "how many microstates lead to the same macrostate" (there is also a natural log in there, but not important for this conversation). This probably doesn't clear up much, but lets do an example, with a piece of iron. 

If you just hold a piece of iron that you mined from the Earth, it will have no, or at least very little, magnetic field. If you take a magnet, and rub it on the piece of iron many times, the iron itself will become magnetic. What is happening? Well, iron is made up of many tiny magnetic dipoles. When iron is just sitting there, most of the time, the little dipoles all face in random, arbitrary directions. You add up all of these tiny little magnetic dipoles and if they are just random, they will, on average, sum to zero. So, no overall magnetic field. 

But when you rub a magnet over the piece of iron, now the little dipoles all become aligned, facing the same direction. Now, when you add all of the individual dipoles together, you don't get zero, you get some number, pointing in the direction the dipoles have aligned. 

So, tying this back into entropy- the non-magnetized iron has high entropy. Why? Well, each of those individual dipoles are one "microstate", and there are many, many options of how to arrange the individual dipoles to get to the "macrostate" of "no magnetic field." For example, think of 4 atoms arranged in a square. To get the macrostate of "no magnetic field" you could have the one in the upper right pointing "up" the one in upper left pointing "right" the bottom right pointing down an the bottom left pointing left. That would sum to zero. But also, you could switch upper left and upper right's directions, and still get zero, switch upper left and lower left, etc. In fact, doing the simplified model where the dipoles can only face 4 directions, there are still 12 options for 4 little dipoles to add to zero. 

But, what if instead the magnetic field was 2 to the right (2 what? 2 "mini dipole's worth" for this). What do we know? We know there are three pointing right, and one pointing left, so they sum to 2. Now how many options are there? Only 4. And if the magnetic field was 4 to the right, now there is only one arrangement that works- all pointing to the right. 

So, the "non magnetized" is the highest entropy (12 possible microstates that lead to the 0 macrostate), the "a little magnetized" has the "medium" entropy (4 microstates) and the "very magnetized" has the lowest (1 microstate). 

The second law of thermodynamics says "things will tend towards higher entropy unless you put energy into the system." That's true with this piece of Iron. The longer it sits there, the less magnetized it will become. Why? Well, small collisions or random magnetic fluctuations will make the mini dipoles turn a random direction. As they turn randomly, it is less likely that they will all "line up" so the entropy goes up, and the magnetism goes down. And it takes energy (rubbing the magnet over the iron) to decrease the entropy- aligning the dipoles.