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0 pointskgwgk3y ago0 comments

> Any state where no particles are in the viscinity of the thermometer is a low probability. All microstates that encompass this property occupy at the 0 temperature macrostate.

Ok. I'm glad to read that we finally agree that in your example -using the macrostate you defined- the entropy of the "particles near a corner" state is not different from the entropy of any other "particles not near the thermometer" state.

Right after you said "Temperature as measured by a thermometer is the macrostate. Every possible configuration of particles (microstates) that causes mercury to rise to a certain degree represents a different macrostate." - I asked "How does your configuration where the balls where near one corner in the cube causes mercury to rise to a different level than the configuration where they occupy a larger volume near the center?"

You could have answered "it doesn't - that's the same macrostate with the same temperature and the same entropy" back then.

Later I pointed out that "Reducing the space occupied by the initial configuration [doesn't change] the temperature - which you say is 0 in all those cases - or the macrostate - which you call absolute zero macrostate in all those cases. The entropy would be the same whenever the particules are more concentrated than in your example - even though they would have lower probability of ocurrence. Don't you agree?"

Instead of answering "I don't agree. Entropy is lower when the current macrostate has a low probability of occuring." you could have said "I agree. I describe the temperature as zero in all those cases, it's the same macrostate and the entropy will be the same."

Better late than never, anyway.

> the word temperature is poorly defined when applied to a box.

I agree! You're the one who picked the reading of that thermometer as the thing that would determine the macrostate and the entropy - and maintained that higher concentrations would mean different thermometer readings and lower entropy.

> If you are in agreement with me that entropy is independent of knowledge then we're good; because as far as I was concerned this was the point you were trying to make.

If we agree that the entropy is not a physical property of (the microstate of) the system but a property of a particular (thermodynamical) description of the system - and that different descriptions of the same physical system are possible resulting in different entropies - we're good. That's the clarification I wanted to make.

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4 comments · 1 top-level

deltasevennine3y ago· 3 in thread

>Ok. I'm glad to read that we finally agree that in your example -using the macrostate you defined- the entropy of the "particles near a corner" state is not different from the entropy of any other "particles not near the thermometer" state.

This has been the definition since I brought it up. That's how thermometers work. It's the obvious consequence of my description and it's how physicall thermometers generally work. You never made it clear that was your problem with it. Well, now that we're both clear there is no problem with it, I think initially it most likely it just didn't jive with your intuition about temperature.

>You could have answered "it doesn't - that's the same macrostate with the same temperature and the same entropy" back then.

I did answer this: "The balls have to touch thermometer. Otherwise the thermometer observes nothing." You failed to pick up on what I meant. If the balls don't touch the thermometer is means "it doesn't" change the thermometer and therefore it doesn't change the macrostate.

You just didn't get it. OK you can accuse me of not explaining it thoroughly. But I can equally at the same time accuse you of not being capable to interpret what I said. I think what's going on here is that you're too stuck in your headspace of thinking that your intuition of entropy was more accurate then mine and you wanted me to come to this realization. I think what happened here is the reverse of this. Your intuition about entropy was less crystallized then mine and most of the communication issues we had was because you thought it was the other way around.

>Instead of answering "I don't agree. Entropy is lower when the current macrostate has a low probability of occuring." you could have said "I agree. I describe the temperature as zero in all those cases, it's the same macrostate and the entropy will be the same."

I told you to refer to my explanation of the macrostate. Yeah in all those cases it will be the same. Ok fine. I could've said that. But I didn't realize that was what you were hung up on. To throw it back at you, you could've said this:

"it doesn't make sense to me that different concentrations of particles in different parts of the box yield the same temperature reading AKA the macrostate. Please explain how this can be possible"

But again I think you didn't realize this was your hang up. I think you thought the my definition of macrostate was a "bad" or something and you were trying to make me realize it?

>I agree! You're the one who picked the reading of that thermometer as the thing that would determine the macrostate and the entropy - and maintained that higher concentrations would mean different thermometer readings and lower entropy.

Yeah I picked it because it's the most intuitive one to illustrate rising entropy. The "2nd law". It's the classic model everyone has in there heads of the "heat death" of the universe.

There are technical issues with the word, but it's the most commonly used one, and we only discussed those technicalities because of a fundamental misunderstanding on your end. IF the intuition was correct, the technicalities do not need to be discussed, or thought about.

>If we agree that the entropy is not a physical property of (the microstate of) the system but a property of a particular (thermodynamical) description of the system -

Sort of. Entropy is directly tied to macrostate, but macrostate is determined by microstates. There is a relationship here from entropy to microstate but not direct.

Also ALL possible macrostate configurations, ARE independent of knowledge of the system. There is no case where knowledge can influence it. There is no case where your initial reply: "If you know the positions and velocities of the balls at all times arguably the entropy is always zero." is correct.

Unless of course you define a macrostate where it's zero all the time. But obviously what you're saying here is that knowledge changes the entropy. Which is not true.

kgwgkOP3y ago

> Entropy is directly tied to macrostate, but macrostate is determined by microstates.

There is not one true macrostate determined by the microstate - it depends on how we chose to describe the system. Your "reading of this thermometer" macrostate is not more real than the "energy" macrostate.

> There is a relationship here from entropy to microstate but not direct.

There is a relationship that depends on what is the thermodynamical model used to describe the system.

> There is no case where your initial reply: "If you know the positions and velocities of the balls at all times arguably the entropy is always zero." is correct.

Theoretically I could make the entropy go as close to zero as I want by making the macrostate more and more detailed. Quantum thermodynamics is one case in which entropy is zero when a state is perfectly known.

> But obviously what you're saying here is that knowledge changes the entropy. Which is not true.

What I'm saying is that "the entropy" doesn't exist outside of our minds. It's the product of our description of the thermodynamical system. Depending on the model that we think of we produce a different entropy.

Coming back to your original question: https://news.ycombinator.com/item?id=33226742

deltasevennine3y ago

>What I'm saying is that "the entropy" doesn't exist outside of our minds. It's the product of our description of the thermodynamical system. Depending on the model that we think of we produce a different entropy.

This whole discussion is pointless. It kind of angers me that we dived into this pointless pedantic side quest. If this is all you're trying to say then clearly when I defined a custom macrostate then you already knew I knew this. Why bother arguing about useless details? I think you're not being entirely honest here. I think you were mistaken about entropy OR you have certain issues going on with you as you spent so much time pushing this pointless thread forward. But whatever.

No offense but this is probably the worst way to describe it. I have a mathematical model of a projectile motion. The projectile motion is a product of my mind because I made up that model. This is a COMPLETELY pointless statement and is analogous to yours.

I think this is snobbery. Either you assumed I didn't know what entropy was and in your snobbery wanted to teach me with some "revelatory" counter examples (which wasted so much time) or YOU didn't know what entropy was and you're just not admitting it.

>There is a relationship that depends on what is the thermodynamical model used to describe the system.

Right before you wrote this you wrote: "entropy is not a physical property of (the microstate of) the system but a property of a particular (thermodynamical) description of the system" which is completely contradictory. There is no way for entropy to ONLY be about macrostate WHEN macrostate is defined in TERMS of microstates.

It's like saying Trees have nothing to with atoms because trees are made of wood. Well guess what? Wood is made out of atoms!

This whole line is contradictory.

>Theoretically I could make the entropy go as close to zero as I want by making the macrostate more and more detailed. Quantum thermodynamics is one case in which entropy is zero when a state is perfectly known.

Wow this whole conversation started because you wanted to make light of some pedantic detail. Yeah if you define macrostate as a microstate sure. But if you want to go pedantic we can, your statement is STILL incorrect in light of your new example. Entropy is not ALWAYS zero if you know position and velocity of the balls, simply because this is not ALWAYS the case.

There are counter examples to your ALWAYS qualifier which makes your statement definitively false.

>Coming back to your original question: https://news.ycombinator.com/item?id=33226742

You have not answered my question. You aren't getting it. Rising Entropy is just an example for illustrative purposes, entropy is simply a probabilistic phenomenon. The question is deeper then that and is about the nature of probability and reality itself.

>Only if we keep adding uncertainty / forgetting information as we go forward will entropy increase.

Bro. Forgetting stuff doesn't change entropy. We already agreed that entropy is independent of knowledge. Yes Entropy is defined generically in that it requires an additional definition of a macrostate in order for the equation to be fully utilized.... but it is still in this case independent of knowledge.

You could say that forgetting stuff requires you to use lower resolution macrostate models in practice but this independent of the theoretical equation and is just a really stupid and over-complicated way of describing it.

For example: you could say that the volume of a rectangular prism is wlh. If someone forgets h, does that change the volume of the prism? Only if that someone is an ass hole (aka philosopher). Don't be an ass hole. This kind of "knowledge" related stuff can literally be applied to everything and is a rabbit hole with no final destination. The heart of it lies deeper.

kgwgkOP3y ago

> You never made it clear that was your problem with it.

Just to be clear, the problem was not with my intuition about temperature. The problem was trying to put toghether

  "all those configurations with no particles near the thermometer -which may be very concentrated or not at all- have the same entropy"

and

  "the entropy is lower the more concentrated the particles".

For example I wrote two days ago: https://news.ycombinator.com/item?id=33206422

"In every single initial configuration the particles will be at some distance from the thermometer and will cause it to read 0 according to you reasoning (until some time passes). I guess they all correspond to the same "absolute zero macrostate". What I still don't see is how do you calculate the entropy using Gibbs entropy formula in such a way that the entropy is lower or higher for some initial configuration depending on the position of the particles."

Or somewhere up this thread I said very clearly "The balls don’t touch the thermometer in either case. You seemed to imply that the higher concentration means a different macrostate with lower entropy."

and you insisted that "Yes. The higher concentration has a lower probability of occurring. And occupies a different temperature reading on the thermometer. Each temperature reading is a different macrostate."

It's not my fault that you insisted that the higher concentration has a lower probability of occurring and occupies a different temperature reading on the thermometer even when I was clearly talking about what you say is the same macrostate with the same temperature.

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4 comments · 1 top-level

deltasevennine3y ago· 3 in thread

>You could have answered "it doesn't - that's the same macrostate with the same temperature and the same entropy" back then.

"it doesn't make sense to me that different concentrations of particles in different parts of the box yield the same temperature reading AKA the macrostate. Please explain how this can be possible"

But again I think you didn't realize this was your hang up. I think you thought the my definition of macrostate was a "bad" or something and you were trying to make me realize it?

Yeah I picked it because it's the most intuitive one to illustrate rising entropy. The "2nd law". It's the classic model everyone has in there heads of the "heat death" of the universe.

>If we agree that the entropy is not a physical property of (the microstate of) the system but a property of a particular (thermodynamical) description of the system -

Sort of. Entropy is directly tied to macrostate, but macrostate is determined by microstates. There is a relationship here from entropy to microstate but not direct.

Unless of course you define a macrostate where it's zero all the time. But obviously what you're saying here is that knowledge changes the entropy. Which is not true.

kgwgkOP3y ago

> Entropy is directly tied to macrostate, but macrostate is determined by microstates.

> There is a relationship here from entropy to microstate but not direct.

There is a relationship that depends on what is the thermodynamical model used to describe the system.

> There is no case where your initial reply: "If you know the positions and velocities of the balls at all times arguably the entropy is always zero." is correct.

> But obviously what you're saying here is that knowledge changes the entropy. Which is not true.

Coming back to your original question: https://news.ycombinator.com/item?id=33226742

deltasevennine3y ago

>There is a relationship that depends on what is the thermodynamical model used to describe the system.

It's like saying Trees have nothing to with atoms because trees are made of wood. Well guess what? Wood is made out of atoms!

This whole line is contradictory.

There are counter examples to your ALWAYS qualifier which makes your statement definitively false.

>Coming back to your original question: https://news.ycombinator.com/item?id=33226742

>Only if we keep adding uncertainty / forgetting information as we go forward will entropy increase.

kgwgkOP3y ago

> You never made it clear that was your problem with it.

Just to be clear, the problem was not with my intuition about temperature. The problem was trying to put toghether

  "all those configurations with no particles near the thermometer -which may be very concentrated or not at all- have the same entropy"

and

  "the entropy is lower the more concentrated the particles".

For example I wrote two days ago: https://news.ycombinator.com/item?id=33206422

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