Understanding the Entropy For Real

I was familiar with the term for more than a decade, but I happen to know that I didn't really grasp it when I attempted to explain it in a platform. After hours of discussion with Chatbots and some extra reading that should have been done in my engineering study years now I recognize the pitfalls that I and many people had been at understanding it.

Simlified formal definition (in statistical mechanics), it is a macrostate property determined by the number of different microstates that matter can be in.

If you are someone who describes it as level of 'disorder' that matter's particles is at. (just like the rest of the world) you are on the wrong path. One who really wanted to understand should start using the term 'unpredictability' instead of 'disorder' to describe it. Because it doesn't say anything about the current disorder level, it only says how many different microstates it can go into, how unpredictable it can behave Just like defined in its format definition. $$S = k_B \ln \Omega$$ Higher the number of the microstates ($\Omega$), higher the enropy will be.

Because two matters that have different entropies can end up exactly in the same particular configuration at a moment, can have same level of disorder.

One very misleading example that I hear since high school is "entropy is like how messy your room is."

a big no.

"Entropy is how many different version your room can have." (pay attention doesn't say anything about the current moment).

So one may wonder, how does it relate to the energy then?

Let's consider two water vapors, with similar internal energy, both at the same T, the first one has high p (pressure) and low entropy (high pressure superheated steam, can be used to push a piston) and the other one has low pressure -as a result- high entropy (low pressure steam, can't do much work).

(left one has higher pressure, lower entropy, they have the same T)

Why is the number of arrangements that a substance's particles can have related to its ability to be used to do work?

Because it gives information about the predictability of its movement, think of the low entopy steam flowing upwards rapidly and pushing the piston, this steam, which is confined to a lesser microstate, can be utilized since we have better idea what its particles will do (lower entropy, lower unpredictability), however, low pressure steam with high entropy, spread over an area, may enter different microstates and gives less information about the direction and location of the energy, you see the particles on the right may collide, then you see the particles on the left vibrating, it's spread over vast area, for this reason it has less potential to be used directly for 'work'.