r6 and I discuss his theory that entropy is subjective

[gustavolacerda]

r6 and I discuss his theory that entropy is subjective

I've never been satisfied with the solutions I've seen to Maxwell's Demon.
I take r6's interpretation of entropy as an agent-dependent quantity related to his knowledge, and a measurement of what one can do with this knowledge: knowledge is power. According to his theory, an all-knowing being (

Comments

[spoonless]

Some physicists used to toy with the notion that entropy is subjective and only refers to our "lack of knowledge" about a system. But from what I understand, computer simulations put and end to that way of thinking. Once it became possible to simulate a large number of interacting objects bouncing around exchanging energy, it became obvious that the entropy of a system is an objective quantity which refers to how many accessible states there are in the system

Accessible States

[r6]

Oh, it’s the number of accessible states. For god’s sake, why didn’t books and web pages say that. I had the impression that it was the number of possible states.

[gustavolacerda]

Thanks for the comment.

I briefly looked over the thread, and I noticed you asked "is entropy defined for a macroscopic particle". I think I know what you're asking here, but I'm not sure so correct me if I misinterpretted. I think what you're asking is: does entropy apply to classical systems which have no constituants small enough for quantum mechanics to play a role? And the answer is yes. Entropy is an entirely classical concept;What I meant was "macroscopic" in the sense ping-pong balls: if we had a huge box in space (zero-gravity vacuum), with billions of ping-pong balls bouncing around in it, could we define entropy based on these observable states

[darius]

ping-pong balls: Yes, though in practice the entropy from microscopic variation would be much greater still.

level of detail: See http://en.wikipedia.org/wiki/Entropy#Counting_of_microstates

[spoonless]

What I meant was "macroscopic" in the sense ping-pong balls: if we had a huge box in space (zero-gravity vacuum), with billions of ping-pong balls bouncing around in it, could we define entropy based on these observable states?

Yes, it's perfectly well defined. But only up to an additive constant which has to do with how finely grained things are. You can always add a constant to the amount of entropy in a system and it's not going to change the dynamics. As long as you're consistant as to what constant you add, it doesn't matter. Kind of like defining a "ground voltage". In quantum mechanics, there's a natural definition for what that constant should be, but that need not be essential to the theory of statistical mechanics; it can be seen just a convenience issue.
It seems to me that entropy is a "statistical" law, rather than a "physical" one: the 2nd law says that any system will tend to end up in the more probable set of states; and without knowledge of the system, one cannot bring it into a less probable set of states (

[gustavolacerda]

Yes, that's right... it's a law that comes entirely from statistics. There are some very basic physical assumptions that go into proving it

which physical assumptions?

[spoonless]

Well, the main one is "ergodicity". There are a few other technical ones I think, but I wouldn't know off the top of my head. Only a few experts on the subject are concerned with what axioms are necessary to prove it, whereas most physicists are satisfied with it as long as it works. It wasn't proven rigorously until a long time after it was accepted as a standard law. And there are, I think, still debates on which axioms are the best ones to use

[gustavolacerda]

Once it became possible to simulate a large number of interacting objects bouncing around exchanging energy, it became obvious that the entropy of a system is an objective quantity which refers to how many accessible states there are in the system.

So what's the solution to Maxwell's demon? r6 and I believe that an all-knowing being could decrease the entropy of the box, while keeping his knowledge the same.

[darius]

But the demon's knowledge must have a physical representation, and to run a full thermodynamic cycle it must reset its memory to be ready for the next cycle. This is a matter of erasing information, or increasing entropy.

i.e. this works only when the demon is outside the system being considered in thermodynamic terms.

[gustavolacerda]

Imagine the Genius being outside of the box.
Since he knows everything about the deterministic system inside the box, his knowledge is the same before and after his trick of making heat flow the "wrong" way, so no resetting of the memory is necessary.

Is the relevant question "could he do it again to the same box?"? Obviously, you can't expect the box to go back to the exact same state as before, but I claim that he could take the box back to a "high entropy" state, and then the heat pump again. His memory is not increasing, and neither is it being erased: it's being updated at every "iteration", in a fully reversible process.

Would you say the entropy of the universe increased as a result of this? What could have happened in the Genius's brain to offset the massive entropy loss due to his heat trick?

[spoonless]

Hmmmm... that's a good question. I think the answer might be that in order to compute what's going to happen in the future for a complicated chaotic system you need to do a computation which increases entropy somehow. But it seems that the answer the this question would be pretty different for classical and quantum systems.

Maxwell's demon is something that I don't understand fully either, and I would definitely like to. Maybe we should both read this book on the subject. I particularly think Zurek has some important things to say about Maxwell's demon. He has a lot of papers on it and its combining it with quantum mechanics and information theory.

[gustavolacerda]

That's the reason I quit physics: someone can go as far as you (and much further) not being able to answer such questions. No offense intended. It just shows that most physicists are not interested in logical consequences of / relationships between their theories. I get the impression that much reasoning physicists do is informal and ad-hoc, and I have no idea how easily they could justify them logically, if at all.

Maybe there is a school of physics where they really emphasize logical foundations? A place where people couldn't be happy unless they knew how to solve such paradoxes...

During sophomore year, it became clear that I wouldn't get what I wanted out of a physics education. It was quite a disappointment, but it seems I made the right decision.

[gustavolacerda]

Hm... maybe my comment wasn't called for. Some of these arguments seem quite involved.

It seems that physics curricula tend survey a bunch of ideas without analyzing their logical relationships to each other.

My approach is more to do learn a little bit, stop... check how it fits with everything.... and *then* proceed. This is the reason why I'm slower than most people: I'm always busy searching for contradictions (and incoherences). It's also the reason why my code is less buggy ;-)

what kind of book is this, btw? Maxwell's Demon's Greatest Hits? It seems each paper is from a different place.

[spoonless]

My approach is more to do learn a little bit, stop... check how it fits with everything.... and *then* proceed. This is the reason why I'm slower than most people: I'm always busy searching for contradictions (and incoherences).

I work very much the same way. I'm by far the slowest physicsist (and thinker in general) that I've met. I try harder to understand the foundations of things before I'm happy with them, and as a consequence it takes me longer than most to learn a subject. Or sometimes just longer to admit that I've "learned it". Although I must confess that over this past year, my standards have been slipping a bit due to necessity. The sheer volume of stuff we have to know how to use has started to outweigh the possibility of understanding any of it fully. So my plan at this point is to go along with the way they want me to learn now, and then go back and learn it to my satisfaction when I get the chance. Hopefully, I won't just keep saying that and never go back. :)

[spoonless]

That's the reason I quit physics: someone can go as far as you (and much further) not being able to answer such questions.

When I took graduate statistical mechanics, the professor brought up Maxwell's demon one day and he said "I don't really understand this, but I'll explain it to the best of my ability." He explained it and then I asked him a few questions similar to the ones you asked. And he said "sorry, I just don't know. You'd have to ask an expert on it." The thing is, physics is a really large subject. Each person has a specialization. While they may understand most of the logical foundations of their specialization, nobody has the time to look into every question in infinite detail.

Maybe there is a school of physics where they really emphasize logical foundations? A place where people couldn't be happy unless they knew how to solve such paradoxes...
I'd say the school of physics that emphasizes logical foundations is "mathematics". Or philosophy, depending on which particular questions your asking about. (see my

[spoonless]

During sophomore year, it became clear that I wouldn't get what I wanted out of a physics education. It was quite a disappointment, but it seems I made the right decision.

Oh, one more thing I meant to say. The thing that attracts me most to physics is that it does pose questions which are so difficult to see the logical implications of. I enjoy sitting down and thinking about "hard" problems where the answer is not immediately obvious. Some of the problems in physics are so non-obvious that they've taken half a century or longer for people to answer. (Mawell's demon being one of those questions. I think it was posed back in the 1800's!). So I guess I've taken the opposite approach. Every time I see a physicist who I think doesn't really understand what he's doing, I see it as an encouragement that I have something to offer the field.