newtonian mechanics - Is the second law of thermodynamics a fundamental law, or does it emerge from other laws?

My question is basically this. Is the second law of thermodynamics a fundamental, basic law of physics, or does it emerge from more fundamental laws?

Let's say I was to write a massive computer simulation of our universe. I model every single sub-atomic particle with all their known behaviours, the fundamental forces of nature as well as (for the sake of this argument) Newtonian mechanics. Now I press the "run" button on my program - will the second law of thermodynamics become "apparent" in this simulation, or would I need to code in special rules for it to work? If I replace Newton's laws with quantum physics, does the answer change in any way?

FWIW, I'm basically a physics pleb. I've never done a course on thermodynamics, and reading about it on the internet confuses me somewhat. So please be gentle and don't assume too much knowledge from my side. :)

Answer

In thermodynamics, the early 19th century science about heat as a "macroscopic entity", the second law of thermodynamics was an axiom, a principle that couldn't be derived from anything deeper. Instead, physicists used it as a basic assumption to derive many other things about the thermal phenomena. The axiom was assumed to hold exactly.

In the late 19th century, people realized that thermal phenomena are due to the motion of atoms and the amount of chaos in that motion. Laws of thermodynamics could suddenly be derived from microscopic considerations. The second law of thermodynamics then holds "almost at all times", statistically – it doesn't hold strictly because the entropy may temporarily drop by a small amount. It's unlikely for entropy to drop by too much; the process' likelihood goes like $\exp(\Delta S/k_B)$, $\Delta S \lt 0$. So for macroscopic decreases of the entropy, you may prove that they're "virtually impossible".

The mathematical proof of the second law of thermodynamics within the axiomatic system of statistical physics is known as the Boltzmann's H-theorem or its variations of various kinds.

Yes, if you will simulate (let us assume you are talking about classical, deterministic physics) many atoms and their positions, you will see that they're evolving into the increasingly disordered states so that the entropy is increasing at almost all times (unless you extremely finely adjust the initial state – unless you maliciously calculate the very special initial state for which the entropy will happen to decrease, but these states are extremely rare and they don't differ from the majority in any other way than just by the fact that they happen to evolve into lower-entropy states).