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The Second Law of Thermodynamics (2011)

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Re: The Second Law of Thermodynamics (2011)

#61

Post by ninetyninenine »

kgwgk wrote: post #60
ninetyninenine wrote: post #58

Earlier quoted context omitted.

>If I shoot a pool ball to strike a heavier second ball which is at rest they will end up moving in opposite directions. If "time were to go backwards" - whatever that means - they would approach at the end one would be at rest. That's seems indeed unlikely with "time going forwards" because we wouldn't be able to do that if we tried (at least not systematically). in a vacuum no ball will ever go to rest if it's movi…

> In a vacuum no ball will ever go to rest if it's moving. When a moving ball hits another massive ball that was in its way it’s pretty safe to assume that it was not moving in a vacuum.

>they would approach at the end one would be at rest.

I'm referring to this. This doesn't happen in space. It's on a table on earth.

Re: The Second Law of Thermodynamics (2011)

#62

Post by kgwgk »

ninetyninenine wrote: post #61
kgwgk wrote: post #60

Earlier quoted context omitted.

> In a vacuum no ball will ever go to rest if it's moving. When a moving ball hits another massive ball that was in its way it’s pretty safe to assume that it was not moving in a vacuum.

>they would approach at the end one would be at rest. I'm referring to this. This doesn't happen in space. It's on a table on earth.

If in “time going forwards” a ball hits another one at rest and you “reverse time” right after the collision won’t the “time going backwards” get that ball in rest again? (You’re the one who mentioned physics being symmetrical.)

The point is that with just two things interacting with “time going backwards” you “predict” unlikely things to “happen” and we know that it’s because the “initial” conditions are the exact ones that would make such things happen. It doesn’t seem a big mystery.

In the “many, many, many, we-don’t-even-know-how-many” things interacting case we would encounter something similar. The “initial” conditions if we had “time going backwards” are much more unlikely and the “outcome” much more unexpected because in reality we don’t know almost anything about the state of the system. But we know that those “initial” conditions are “special” - it’s not more mysterious than the simpler case.

Re: The Second Law of Thermodynamics (2011)

#63

Post by vinnyvichy »

082349872349872 wrote: post #53
vinnyvichy wrote: post #22

Earlier quoted context omitted.

I'm pretty sure I don't understand the possible meanings of what you said there either so let's try :) I meant that the tangent to the convex conjugate ("momentum") provides bounds on what the values returned by the dual step in a primal-dual algo should be. I don't know which meaning of "exponential" I should focus on here (the action perhaps? A power set? A probability distribution?), but "implications" seem to ref…

That makes much more sense than my flash, which had been following a spark in the other direction: Delimited continuations are functions, and as such (in a world of algebraic types where we can take sums and products of types) exponentials of types, ran^dom. [in particular, with the substitution of isomorphism for equality they follow the normal K-12 rules: C^(A+B) ~= C^A * C^B, etc.] I'd just been glancing at https:…

:)

I'm guessing you might have wanted to sloganize that as: "DC's are algebraic" https://cstheory.stackexchange.com/questions/42431/how-to-te...

This reverse flash might be what could motivate me to make the connection useful.. an exercise in geometric vengeance (and intuition building) for me to use backtracking DCs in optimization problems (engineering => SDP/IPs)? now to find a plug-and-chug example..

A bunch of timely puns here, including "thermometer continuations" https://arxiv.org/pdf/1710.10385

Besides negative T occuring in situations where the arrow of t appears reversed..., PG13 "exponentials turn products into sums"

There is also the pun where S stands for both "action" and "entropy" so that's another direction in which to hunt for the Lagrange multiplier/Lagrangian-Hamiltonian connecting unicorn e.g. picking the "most representative", not necessarily the most optimal path.

Re: The Second Law of Thermodynamics (2011)

#64

Post by kgwgk »

mlsu wrote: post #55
ninetyninenine wrote: post #40

Earlier quoted context omitted.

This is what confuses people. There is this universal law, but you already know about it. It's probability. Increasing Entropy is a result of probability. That's all it is. When you have a bunch of particles and you jostle the particles it is MORE probable for the particles to become spread out then it is to become concentrated in one corner. That probability is what is behind this mysterious force called entropy. Wh…

this is great and it does make perfect sense to me, someone with no stat thermo background. but it makes me wonder how is it then, that things are becoming more spread out over time? what is the property about the past, that it seems have a lot of uncommon states and not a lot of the common ones? if common states are mathematically more likely to be common, why is it that the future has them and the past does not, in…

> how is it then, that things are becoming more spread out over time?

This may help: https://www.researchgate.net/figure/Classical-evolution-in-p...

If we knew the present we could predict the future - at least in classical physics. We have a very approximative knowledge of the present though, based on a macroscopic description. We can still predict a range of outcomes and see what it means in macroscopic terms. The initial set of states consistent with what we know “spreads out” as time goes by. We “lose” information by keeping only a “coarse” macroscopic description.

Re: The Second Law of Thermodynamics (2011)

#65

Post by cubefox »

stonemetal12 wrote: post #45
cubefox wrote: post #39

There is also an interesting relation between the second law of thermodynamics and the cosmological principle (which says "the distribution of matter is homogeneous and isotropic on large scales"): The second law of thermodynamics says that the universe has an entropy gradient in the time dimension, while the cosmological principle says that the universe has no matter gradient in the spatial dimensions. So together t…

>merely called a "principle" Merely a principle? In science principles are what mathematicians call Axioms. Not proven but taken as true because you have to start somewhere, and it is the only thing that makes sense. The cosmological principle is the philosophical position that physics works the same everywhere. We haven't done physics experiments across the universe, so we can't call it a law because there is not en…

You are confusing the cosmological principle with the uniformitarian principle [1]. The cosmological principle concerns the large-scale distribution of matter (not of laws) in the universe, and that is something we arrived at empirically, through observations with large telescopes (galaxies are approximately equally distributed in all directions) and the measurement of the cosmic microwave background. It doesn't get more empirical than that. It's not something like an axiom at all, just an approximate generalization.

> We haven't done physics experiments across the universe, so we can't call it a law because there is not enough experimental evidence.

That's equally true for the second law of thermodynamics: We haven't done physics experiments in the distant past or in the future direction, so we strictly speaking can't be certain that entropy doesn't decrease in the future. But no law is perfectly confirmed anyway (not tested in every conceivable circumstance), so that can't be a criterion for lawhood anyway.

But I already proposed a better criterion: A (fundamental) law says what is possible and impossible, and neither the cosmological principle nor the second law ("law") of thermodynamics do that.

[1] https://en.wikipedia.org/wiki/Uniformitarianism

Re: The Second Law of Thermodynamics (2011)

#66

Post by passion__desire »

mlsu wrote: post #55
ninetyninenine wrote: post #40

Earlier quoted context omitted.

This is what confuses people. There is this universal law, but you already know about it. It's probability. Increasing Entropy is a result of probability. That's all it is. When you have a bunch of particles and you jostle the particles it is MORE probable for the particles to become spread out then it is to become concentrated in one corner. That probability is what is behind this mysterious force called entropy. Wh…

this is great and it does make perfect sense to me, someone with no stat thermo background. but it makes me wonder how is it then, that things are becoming more spread out over time? what is the property about the past, that it seems have a lot of uncommon states and not a lot of the common ones? if common states are mathematically more likely to be common, why is it that the future has them and the past does not, in…

> what is the property about the past, that it seems have a lot of uncommon states and not a lot of the common ones?

This is called as Past hypothesis.

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

Re: The Second Law of Thermodynamics (2011)

#67

Post by Iwan-Zotow »

robaato wrote: post #29

The classic Flanders and Swann explanation: https://www.youtube.com/watch?v=VnbiVw_1FNs Excerpts: No one can consider themsleves educated who doesn't understand the basic language of science - Boyle's law: the greater the external pressure the greater the volume of hot air. I was someone shocked to learn my partner not only doesn't understand the 2nd law of thermodynamics, he doesn't even understand the first! : Heat…

thanks, good one

Re: The Second Law of Thermodynamics (2011)

#68

Post by gavindean90 »

ninetyninenine wrote: post #47
gavindean90 wrote: post #46

Earlier quoted context omitted.

I don’t buy it. You can’t say entropy is probability and then say but we don’t know what probability really is. It’s both foundational to physics and computer science. I could say probability is really just entropy just as easily. I would go farther and say that time is entropy as we measure time by observing entropy.

you don't buy it? This is foundational. This isn't something I'm making up. It's the formal definition of entropy. https://www.labxchange.org/library/items/lb:LabXchange:ac117... .

Thanks for linking that. My point really was that entropy is many things and probability is among them.

Re: The Second Law of Thermodynamics (2011)

#69

Post by mlsu »

ninetyninenine wrote: post #57
mlsu wrote: post #55

Earlier quoted context omitted.

this is great and it does make perfect sense to me, someone with no stat thermo background. but it makes me wonder how is it then, that things are becoming more spread out over time? what is the property about the past, that it seems have a lot of uncommon states and not a lot of the common ones? if common states are mathematically more likely to be common, why is it that the future has them and the past does not, in…

>how is it then, that things are becoming more spread out over time? It's more likely for things to spread out then to concentrate in one corner when you randomly move all particles in a box. If all particles moved to one corner of a box you would assume there's an intelligence at work moving the particles because such movement is too low of a probability to happen without intelligent intervention. >if common states…

But that's a semantics game. Sub probability for entropy. Why do we live in a world where low probability states were in the past and high probability ones are in the future? What intrinsic property of the universe causes this asymmetry? One can imagine a symmetric k-negative universe where high probability macrostates trend towards low probability macrostates. Or a k-zero universe where the dice never rolls.

None of such questions follow definitionally from the second law ^H^H^H probability.

Re: The Second Law of Thermodynamics (2011)

#70

Post by ninetyninenine »

mlsu wrote: post #69
ninetyninenine wrote: post #57

Earlier quoted context omitted.

>how is it then, that things are becoming more spread out over time? It's more likely for things to spread out then to concentrate in one corner when you randomly move all particles in a box. If all particles moved to one corner of a box you would assume there's an intelligence at work moving the particles because such movement is too low of a probability to happen without intelligent intervention. >if common states…

But that's a semantics game. Sub probability for entropy. Why do we live in a world where low probability states were in the past and high probability ones are in the future? What intrinsic property of the universe causes this asymmetry? One can imagine a symmetric k-negative universe where high probability macrostates trend towards low probability macrostates. Or a k-zero universe where the dice never rolls. None of…

Yes. It is a semantics game. I feel people understand probability but they don't understand entropy hence it's easier to just use the term probability state.

And yes the questions you pose don't follow from the 2nd law. But they are the big question.

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