system
Given the following post, respond as if you're commenting on Reddit:
human
Why does entropy have to increase?

I don't understand the second law of thermodynamics. I mean I think I understand what it says, but I don't understand why it's true. Is there a way to (mathematically) prove that net entropy necessarily increases in a closed system or is this just something we've observed and therefore assume to be true in all cases?

Also, if we assume that systems are on a linear path from order to chaos, wouldn't that have to mean that in the beginning, the universe was in a state of perfect order? The commonly accepted theories on how the universe came into being seem to contradict this, because (as far as I know) right after the big bang the universe was filled with gluon plasma which then developed into orderly systems like galaxies. Or is a universe filled with gluon plasma considered to be more orderly than a universe of galaxies? If so, why? 

I think my core problem is the definition of "order".
gpt
Let's talk about microstates and macrostates. Macrostates are the outward appearance of a system, and microstates are the internal arrangement (someone post better definitions if you want). So if our system is two dice, the macrostate is the sum of the roll, and the microstates are the individual numbers. If our macrostate is 7, our microstates are 1-6, 2-5, 3-4, 4-3, 2-5, and 6-1. If we roll an 11, there are only 5-6 and 6-5. Six microstates for the 7 macrostate, but two for the 11.

If all microstates are equally likely, then statistically the system will be found in the macrostate that has the most microstates. If there are a large number of particles, then the system reaches that state quickly and is unlikely to leave.

Keep in mind that this is a statistical effect; there can be local temporary violations.