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It took me 10 years to understand entropy

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Re: It took me 10 years to understand entropy

#221

Post by mannykannot »

jbay808 wrote: post #214
mannykannot wrote: post #207

Earlier quoted context omitted.

If two people disagree on the maximum amount of work that could be extracted from a given system (with both of them basing their figure on their own evaluation of S), are there any cases where it would it be impossible to empirically demonstrate that at least the proponent of the lower figure was wrong? If only changes in S (and F) have measurable consequences, would that not merely mean that assigning an absolute va…

> are there any cases where it would it be impossible to empirically demonstrate that at least the proponent of the lower figure was wrong? Isn't it more interesting to examine a situation where it would be possible to empirically demonstrate that the proponent of the lower figure was wrong?

In that case we could objectively say that one value of S does not yield F for that system (given that F is defined as a maximum), but this would not resolve the general question of subjectivity.

Re: It took me 10 years to understand entropy

#222

Post by jleyank »

lvncelot wrote: post #69
ravi-delia wrote: post #31

Earlier quoted context omitted.

I'm still mad about top and bottom when truth and beauty were right there !

If I'm not mistaken, the "official" names are just "t" and "b", so top and bottom, just like truth and beauty, are more mnemonics. So referring to them as truth and beauty would be just as correct.

Thought one was their names and the other their attributes?

Re: It took me 10 years to understand entropy

#223

Post by kgwgk »

Jensson wrote: post #217
kgwgk wrote: post #215

Earlier quoted context omitted.

> Depends if you do classical statistical physics or quantum. If you do classical they all have the same energy. That's just completely wrong. With all due respect, you should (re?)learn the classical statistical physics :-) https://en.wikipedia.org/wiki/Boltzmann_distribution

That is for a subset of a larger system, not for a closed system. A closed system has fixed energy in classical. So for example, if you have a gas as a closed system, takes a part of that, then you can measure that parts energy distribution by just accumulating the different micro states, yes. But if you view that part as a closed system, then if it has higher energy then it has higher temperature (if it is in the sa…

> A closed system has fixed energy in classical.

Wrong again!

https://en.wikipedia.org/wiki/Closed_system

"In thermodynamics, a closed system can exchange energy (as heat or work) but not matter, with its surroundings."

Maybe you meant "isolated" instead of "closed" - but then I don't know what we have been talking about. (When I say "we" I mean "you".)

> It doesn't make sense to count the microstates for a volume of gas at some pressure and temperature.

A volume of gas at some pressure and temperature is a closed system but not an isolated system.

> I can have a container with 1l of some gas at room temperature T1 and proceed to heat the room - and the container - to temperature T2.

The containers in that example are closed systems but not isolated systems.

> the microstates of that sample of gas at some fixed temperature don't have all the same energy

That sample of gas at some fixed temperature is a closed system but not an isolated system.

Hopefully you'll agree with everything I wrote with the understanding that we were not talking about isolated systems.

[ have _you_ tried reading a physics book? :-) ]

Re: It took me 10 years to understand entropy

#224

Post by alimov »

brabel wrote: post #131
alimov wrote: post #76

Earlier quoted context omitted.

> The article describes it as a measure of hidden information in a system, which is a good description. But that's not a property of the system itself, it's a property of the observer, from whom the information is hidden. Was hoping to see someone point this bit out.. I wish references to entropy included this piece of information more frequently. When I was first trying to understand the concept I kept thinking of i…

Speaking of observers always rubs me off the wrong way... I don't want to touch on the observer problem, but just to mention something that should be obvious: there's ALWAYS hidden information in any system where time exists. Any "observer" can only know what the world looks like within its light cone. Because quantum mechanics shows that determinism is not possible, it's not possible for any "observer" to know the e…

Since entropy seems to be a measure of our ignorance, then there maybe there is no point in discussing a perfect observer (of something that is boundless). Edit: > talking about a "perfect observer" that knows all there is to know makes absolutely no sense.

if there was such a thing as a perfect observer, let’s say it is you, then you would still choose to measure some things, but not others. Unless by “perfect observer” you are referring to something that knows the states of all things simultaneously at all times, in which case that (to me) doesn’t sound like an observer at all, would just be someone/something that knows. So like you said “there is always hidden information” but that information is hidden to someone that is doing the observing and so is dependent on them. Otherwise from what or whom would the information be hidden? What would information even be without an observer?

Re: It took me 10 years to understand entropy

#225

Post by deltaonefour »

kgwgk wrote: post #196
deltaonefour wrote: post #186

Earlier quoted context omitted.

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 mic…

> 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.

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.

Re: It took me 10 years to understand entropy

#226

Post by deltaonefour »

jbay808 wrote: post #195
deltaonefour wrote: post #186

Earlier quoted context omitted.

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 mic…

> 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.

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

Re: It took me 10 years to understand entropy

#227

Post by kgwgk »

deltaonefour wrote: post #225
kgwgk wrote: post #196

Earlier quoted context omitted.

> 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.

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.

"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.

Re: It took me 10 years to understand entropy

#228

Post by jbay808 »

deltaonefour wrote: post #225
kgwgk wrote: post #196

Earlier quoted context omitted.

> 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.

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.

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?

Re: It took me 10 years to understand entropy

#229

Post by jbay808 »

deltaonefour wrote: post #226
jbay808 wrote: post #195

Earlier quoted context omitted.

> 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.

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

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.

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.

Re: It took me 10 years to understand entropy

#230

Post by deltaonefour »

jbay808 wrote: post #229
deltaonefour wrote: post #226

Earlier quoted context omitted.

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

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 . You can read the thermom…

But entropy does not change with this knowledge.
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