It took me 10 years to understand entropy

What I'm seeing in your other reply is actually you not even reading my reply. Your making statements on things I already touched upon.

It makes you seem not intelligent. But that would be a rude thing to say would it? There's no point. If you want to have a discussion probably smart to say things that will keep the other person engaged rather then pissed off.

This is actually bad enough where I demand an apology. Say your sorry, genuinely, or this thread won't continue and you're just admitting your mean.

We did agree. I never said otherwise. Where are you getting this idea? I'm saying our agreement on this fact is useless. Why don't you actually fully read what I wrote.

>I was trying to say that the inputs to S(...) are the things that we know because we did measure them or set their values. It seems that we agree on that because it's extremely obvious.

I spent paragraphs remarking on this ALREADY. I get what your saying. You're not even reading what I wrote. Every mathematical model has this property you describe. It is not unique to entropy. If you don't know the parameters of even the Pythagorean theorem, then you can't calculate the length of the hypotenuse. Does this mean the pythagorean theorem depends on your knowledge of the system? Yes but kind of a pointless thing right? If this is the point your trying to make, which I highly doubt, then why are we focusing only on entropy? Because knowledge of any system is REQUIRED for every single mathematical model that exists or the model is useless.

I don't think your clear about the argument either. If your not talking about knowledge as a quantifiable input parameter then I don't think your clear about what's going on.

>I fully acknowledge that we may choose to ignore the additional knowledge and keep using the old model - and it may be good enough for some uses.

Entropy is used with full knowledge that it's an fuzzy model. It's based on probability. It doesn't matter if we "ignore" or don't know the additional properties of the model. The model doesn't incorporate that data regardless of whether that information is known or not known.

>They were the same in my example. Same volume. Same temperature. Same pressure.

No. The boltzman distribution changes with gas type as well. The models are different.

>For an ideal gas doubling the volume and the number of particules

In this case yes. But only for an ideal gas. I don't recall if you mentioned the gases were both ideal. Let me check. You did mention it. But then you mention the gases are different. Hydrogen and helium. Neither gas is technically ideal, and the quantum mechanical effects would likely influence the boltzman distribution when mixed. There are contradictions in your example that make it not clear.

>https://en.wikipedia.org/wiki/Gibbs_paradox

The article you linked explains it away. It's the choice of Macrostates, effects the entropy outcome. The article says it's subjective in the sense that it's your choice of Macrostates. The Macrostates don't change based off your knowledge. You choose the one you want.

Yes. A probability distribution can still be derived from a series of events EVEN when the outcome of those exact events are known prior to the actual occurrence.

I believe this is the frequentist view point as opposed to the bayesian viewpoint.

The argument comes down to this as entropy is really just a derivation from probability and the law of large numbers.

If I can look at a probability distribution from data collected from the past and generate a probability. Why can't I look to the future and do the same thing? Even with knowledge of the future you can still count each event and build up a probability from future data.

Think of it this way. Nobody looks at a past event and says that the probability of that past event was 100%. Same with a future event that you already know is going to occur. The probability number is communicating frequency of occurrence along along a large sample size. Probability is ALSO independent of knowledge from the frequentist viewpoint. Entropy is based off of probability so it is based off this concept. Knowledge of a system doesn't suddenly reduce entropy because of this.

Not offended by your words but I am offended by the way you think. Maybe rather then assuming I'm wrong and your superior, why don't you just ask questions and dig deeper into what I'm talking about.

Probability is a mathematical concept separate from reality. Like any other mathematical field it has a series of axioms and the theorems built off the axioms are independent of our typical usage of it in applied applications.

Just because it's rare for probability to be used on future events that are already known doesn't mean the math doesn't work. We tend to use applied math, specifically probability, to predict events that haven't occurred yet but the actual math behind probability is time invariant. It can be applied to events that have ZERO concept of time. See Ulam spirals. In Ulam spirals prime numbers have higher probability in appearing at certain coordinates. This probability is determined independent of time. WE have deterministic algorithms for calculating ALL primes. Yet we can still write out a probability distribution. Probability still has meaning EVEN when the output is already known.

That means I can look at a series of known past events and calculate a probability distribution from there. I can also look at a series of known future events and do the same thing. I can also look at events not involving time like where prime numbers appear on a spiral and calculate a distribution. Just look at the math. All you need are events.

English and traditional intuitions around probability are distractions from the actual logic. You used an english sentence to help solidify your point but obviously our arguments are way past surface intuitions and typical applied applications of probability.

Look up frequentist and bayesian interpretations of probability. That is the root of our argument. You are arguing for the bayesian side, I am arguing for frequentist.