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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

#241

Post by raattgift »

jbay808 wrote: post #146
andi999 wrote: post #81

Earlier quoted context omitted.

Entropy (differences) are an objective quantity which can be measured, there is no subjectivity about it. It is not which parameters you know it is about which parameters you hold fixed.

No, it is subjective. We just only have such blunt instruments for practically measuring states, relative to the gargantuan amount of entropy in most real systems, that the subjective nature of entropy is easy to miss. But in a world where the frontiers of thermodynamics have moved from steam engines to lasers, computers, DNA, and black holes, the difference is increasingly obvious and important. With steam engines,…

Maybe better to say that the universe does not appear to pick out a single coarse-graining or fine-graining procedure for practically any system.

For instance, following your Boltzmannian example, I think one would notice swapping 1 µm³ of the r/w head and 1 µm³ of the recording surface of a new, freshly powered on HDD more than one would notice substituting the entire HDD for a new one of the same model and turning that on. And here I am already using units of length (cf. "equal volume"), and we know neither units nor lengths are generally picked out by the universe.

Re: It took me 10 years to understand entropy

#242

Post by andrewflnr »

XorNot wrote: post #39
andrewflnr wrote: post #18

Earlier quoted context omitted.

OP is about as good as any explanation I've seen.

"Compressibility" (in the software sense) would perhaps carry the most meaning. Entropy is ultimately all about the ability to extract information (i.e. work) out of a system.

"Compressibility" is really not that great an illustration for physical entropy. Information-theoretic entropy is not quite the same thing as physical entropy, but close enough to confuse you if you're not paying attention.

Re: It took me 10 years to understand entropy

#243

Post by stazz1 »

AnthonyAguirre wrote: post #165

Actually a quite nice article. After also spending years as a professional physicist not understanding entropy, I finally decided that I was not necessarily the problem, and spent the last 5 years or so trying to understand it better by rewording the foundations with my research group. (I'm one of the papers the author cites is part of a series from our group developing "observational entropy" in order to do so.) A l…

The universe is an open system.

Re: It took me 10 years to understand entropy

#245

Post by im3w1l »

omegalulw wrote: post #235
kgwgk wrote: post #234

Earlier quoted context omitted.

Physical entropy is defined from the probability distribution over states. Velocities or squared-velocities are not states, they are derived quantities. Points in a phase space would describe states. Physical states are discrete anyway when you consider quantum physics :-) As for the entropy of probability distributions in general, I think relative entropy is invariant under reparametrizations because both the probab…

+1. The commenter above also wanted cared about bijective mappings, and squaring a random variable in [-1, 1] is not bijective. Squaring a random variable defined over positive real numbers would lead to a bijective mapping and the distribution would still remain uniform. Actually, I find it hard to come up with a bijective mapping that leads to a non uniform distribution that's useful for anything practical.

Ok so first to have a uniform distribution we have to have a bounded set. Maybe you can do something clever with limits but lets not overcomplicate things. Lets say we have 0 Uniformity of v would mean that p(0 Uniformity of E would mean that p(0 But by construction p(0 <= v < 1) = p(0 <= E < 1). So it's not possible for both to be uniform.

Re: It took me 10 years to understand entropy

#246

Post by deltaonefour »

jbay808 wrote: post #232
deltaonefour wrote: post #230

Earlier quoted context omitted.

But entropy does not change with this knowledge.

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…

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.

Re: It took me 10 years to understand entropy

#247

Post by deltaonefour »

jbay808 wrote: post #228
deltaonefour wrote: post #225

Earlier quoted context omitted.

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?

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.

Re: It took me 10 years to understand entropy

#248

Post by deltaonefour »

kgwgk wrote: post #227
deltaonefour wrote: post #225

Earlier quoted context omitted.

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 fi…

>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.

Re: It took me 10 years to understand entropy

#249

Post by [deleted] »

deltaonefour wrote: post #246
jbay808 wrote: post #232

Earlier quoted context omitted.

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…

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 N…

[deleted]

Re: It took me 10 years to understand entropy

#250

Post by lvncelot »

jleyank wrote: post #222
lvncelot wrote: post #69

Earlier quoted context omitted.

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?

Seems like you're right and I misremembered.
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