[jbay808]

> Even if I knew the exact position of all atoms in a cup of water, the temperature of that water does not change due to that knowledge.

It actually does! You would disagree with the other person about the temperature of that water. But I agree that this is admittedly not obvious at first.

[deltaonefour]

No it does not. The thermometer does not change based off of my knowledge or opinion.

[jbay808]

A thermometer doesn't measure temperature any better than a meterstick measures length. And we all know what Einstein had to say about the relativity of metersticks.

To paraphrase from the paper I linked in another reply to you, a thermometer is just a heat bath equipped with a pointer which reads its average energy, whose scale is calibrated to give the temperature T, defined by 1/T = dS/d<E>.

You can read the thermometer if you like, but if you know the exact microstate of the water to begin with, the thermometer reading will tell you much less than you already knew about the water. And precise knowledge of the water's microstate will (theoretically) allow you to extract much more work from that water than you would be able to with only the thermometer reading.

[deltaonefour]

But entropy does not change with this knowledge.

[jbay808]

You seem pretty convinced. Let me see if you're talking about the same pedantic distinction that oh_my_goodness was.

A: "an urn containing either a white ball or a black ball".

B: "I notice that the ball in the urn A is white".

I would say that initially the entropy of our ball-urn system is 1 bit, and that with observation B, we have reduced the entropy of our ball-urn system to 0 bits.

But if you are going to take the view that even knowing the ball in this particular urn is actually white doesn't change the fact that the entropy of <<"an urn containing either a white ball or a black ball">> is 1 bit and not 0, and that that's the entropy that we're discussing, then I won't argue about it any further.

Except for the obligatory xkcd: https://xkcd.com/221/

[deltaonefour]

No I'm not saying that.

The entropy of the system was always 0 bits. Knowledge is irrelevant.

If the urn actually contained nothing and would materialize a black or a white ball randomly then this can occur with or without your knowledge. When the ball materializes and nothing more can be done THEN the entropy has changed. Because there's no more possible microstates.

You not having knowledge about microstates DOES NOT change available microstates. You seem to think that if you don't know about something, anything goes.

You're really arguing abstract philosophy. Did a tree in the forest fall if no one was around to see it? Yes it did dude. Your knowledge of it has nothing to do with whether it fell. Same with entropy. And if you deny the fact that a tree in the forest never fell, then you're the one going off onto a pedantic tangent.

[kgwgk]

I'm surprised to hear that "the entropy of the system was always 0 bits."

Let's say that the urn contains a ball that changes its color from black to white and viceversa every thousand years (relative to January 1, 1970 midnight UTC).

Given that "macrostate" there are two possible and equally probable "microstates". The entropy is positive. If I look into the urn and find that the ball is white was the entropy of the system always zero? Or is it always positive in this example?