[deltaonefour]

No this is completely and utterly wrong. Entropy is not a function of knowledge.

Two people with varying and different levels of knowledge of a system does not mean the system has two different entropy values. 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.

Entropy does rely on what your picked configuration of macro states and microstates. Temperature is an arbitrary choice of macrostate.

[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]

> 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.

If you knew the exact position of all atoms in a cup of water you wouldn't assign any temperature to it. Not a thermodynamic temperature at least.

[deltaonefour]

The number of microstates does not change, even if you KNOW the the cup of water is in a specific microstate.

The boltzman equation is based on total accessible microstates.

[kgwgk]

"accessible" means something only given a set of constraints.

Like the temperature, if you keep the temperature of the water fixed. And the number of molecules if instead of a cup you have a close container to prevent it from evaporating. Then what you have is water at some temperature that you control. And you could have the water at a different temperature with exactly the same microstate.

Or imagine gas at some fixed temperature within a cylinder with one movable wall. If you knew the location of every molecule of the gas it wouldn't make sense to talk about its pressure - you could compress it (reducing the number of accessible microstates) without doing any work.

Edit: In summary, thermodynamics loses its meaning if you know the microstate and can act on that knowledge.

[deltaonefour]

>it wouldn't make sense to talk about its pressure -

If I have a pressure gauge that reads the same thing regardless of my knowledge how is pressure meaningless? The tool that reads pressure gives me an accurate pressure number regardless of what I know or don't know. This number is correct.

Your argument is basically saying that the pressure gauge becomes wrong once you have more knowledge of the system. No it doesn't. The pressure gauge is still giving you a number defined as "pressure."

The gas in that cylinder is at a specific microstate within the macrostate defined as pressure.

[kgwgk]

> The pressure gauge is still giving you a number defined as "pressure."

As long as you define “pressure” as “the reading of the manometer” and not as “the variable that together with temperature specifies the state of the gas and measures the quantity of energy required to compress it further”.

Thermodynamics is based on state variables giving a complete description of the system. Statistical mechanics is based on looking at the ensemble of microscopic descriptions possible given what is known about the system and their probabilities.

If all you know is a handful of thermodynamic variables that ensemble is huge. If you know already the microscopic description of the physical system your ensemble has one single possible configuration in it.

As in jbay808’s xkcd example, if you have a random number generator and you know the sequence of numbers that will be generated, do you have a random number generator? The random number generator is still giving you a number defined as “random”, right?

I guess that it’s still random if you “forget” that you know it in advance and that the macrostate is still meaningful as a complete description of the physical system if you “forget” that you have a perfect knowledge of its state.

Edit: the GPS receiver in my phone is giving me some coordinates defined as “position” that happen to be in the middle of the road. However, I know precisely where I am. Don’t you think that the meaning of that “position” is somehow affected by this additional information?

[deltaonefour]

>Edit: the GPS receiver in my phone is giving me some coordinates defined as “position” that happen to be in the middle of the road. However, I know precisely where I am. Don’t you think that the meaning of that “position” is somehow affected by this additional information?

No it is not affected by it. The meaning of position is never changed. Your knowledge of your position can change, but your actual position exists regardless of your knowledge or inaccuracies of your tools.

>As in jbay808’s xkcd example, if you have a random number generator and you know the sequence of numbers that will be generated, do you have a random number generator? The random number generator is still giving you a number defined as “random”, right?

Random number generators are a rabbit hole. There's not even a proper mathematical definition for it. We're not sure what a random number is... we just have an intuition for it. Case in point, the xkcd article could not define it mathematically. This is the reason why the joke exists, because we're not even truly sure what it is or if random numbers are a thing. We have intuition for what a random number is but this is likely some kind of illusion similar to the many optical illusions produced by our visual cortex. If formalization of our intuitions are not possible then there is likelihood that the intuition is not even real.

>Statistical mechanics is based on looking at the ensemble of microscopic descriptions possible given what is known about the system and their probabilities.

ok take a look at this: https://math.stackexchange.com/questions/2916887/shannon-ent...

They're talking about deriving the entropy formula for fair dice. But they talk about it as if we don't have knowledge about physics, momentum and projectile motion. We have the power to simulate the dice in a computer simulation and know the EXACT outcome of the dice. The dice is a cube and easily modeled with mathematics. So then why does the above discussion even exist? What is the point of fantasizing about dice as if we have no knowledge of how to mechanically calculate the outcome? The point is they chose a specific set of macrostates that have uniform distribution across all the outcomes. It is a choice that is independent of knowledge.

[jbay808]

If the cup of water is in a specific microstate at time t=0, and evolves over time according to deterministic equations of motion, how will it "access" other microstates that aren't along that specific trajectory in phase-space?

[deltaonefour]

It can't. But you're not typically defining ONLY microstates along that trajectory as accessible. You are defining all accessible configurations according to your defined macrostate.

Knowledge of future microstates does not change what was already defined as a macrostate. The definition and the rules you used to construct a macrostate are independent to knowledge of the system.

If you gain knowledge of the system and you would like to change your macrostate, then be my guest. You can certainly do that, but "entropy" as we know it does not actually change with more knowledge unless you change the parameters according to your gained knowledge.

Think of it this way. The thermometer ALWAYS reads the same thing EVEN if you have 100% knowledge of the current microstate. You can build a new thermometer using some other mechanism to get a different reading and to take advantage of your new found knowledge... but you'd be changing the definition of your macrostate.