Question on entropy

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Re: Question on entropy

#41  Postby newolder » Jun 16, 2019 8:44 pm

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Jus fixin' teh kaos, boss...
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Re: Question on entropy

#42  Postby Spearthrower » Jun 16, 2019 8:52 pm

Wizardry!
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Re: Question on entropy

#43  Postby hackenslash » Jun 24, 2019 1:55 pm

Blip wrote:I'm hoping for some help from one or more of the physicists here.

Some of you know that I'm doing a course on astrophysics with Oxford ContEd. I don't have a maths or physics background, but the course is designed to be accessible to a wide range of people, and so it is. Mostly.

However, I've come across something which I don't understand and with which our tutor's answer hasn't really helped me. Looking at results from Hubble, it seems that the most distant, i.e. oldest galaxies 'look strange – smaller, irregular, lacking clearly defined shapes.'

Nearer, i.e. more recent galactic views show more ordered galaxies; as that site explains '[c]loser in, we see numerous galaxy interactions and collisions as galaxies come together and merge, growing in the process. And nearer still, we see versions of the large, stately galaxies we know today. '

Help! How does this square with the entropy of the universe increasing?


Because gravity is an ordering force that increases entropy. The more ordered galaxies actually represent an increase in entropy, not a decrease.

This is the problem with equating entropy and disorder. Disorder is a good description of high entropy only in very specific circumstances, because it's a measure of the probability of a given configuration. Thus, because a disordered system is more probable than an ordered one, the disordered system is the one with higher entropy. This does not mean, however, that disorder and entropy are the same thing (this is another conflation of map with terrain, such as humans seem to be fond of).

Properly, entropy is the tendency of energy gradients downwards, and a system whose entropy is higher is one which is closer to its lowest energy state. Entropy is really a measure of how much energy in a system is unavailable for performing work or, in the terms I've presented here, how much energy is further down the gradient than it would need to be to perform work (where work is the equalisation of differentials).

More here:

Order! Order!

And especially here:

All Downhill From Here

As for the deck of cards thing, in reality, an ordered deck has only slightly lower entropy than a shuffled one. Such a system has greater entropy if the deck is scattered around the room. The reason for this is that, because it requires work to put the deck in order, entropy has been brought lower locally at the expense of an increase in entropy less locally, because energy has been expended in ordering it, and is thus unavailable for performing work.
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Re: Question on entropy

#44  Postby romansh » Jun 24, 2019 6:43 pm

hackenslash wrote:
As for the deck of cards thing, in reality, an ordered deck has only slightly lower entropy than a shuffled one. Such a system has greater entropy if the deck is scattered around the room. The reason for this is that, because it requires work to put the deck in order, entropy has been brought lower locally at the expense of an increase in entropy less locally, because energy has been expended in ordering it, and is thus unavailable for performing work.

I could spend five minutes working, continually shuffling the cards or I could spend five minutes putting them in order. Which "system" would have the higher entropy? Assuming the same "work" goes into ordering and shuffling?
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Re: Question on entropy

#45  Postby scott1328 » Jun 24, 2019 8:24 pm

romansh wrote:[Assuming the same "work" goes into ordering and shuffling?

That is a bad assumption.
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Re: Question on entropy

#46  Postby romansh » Jun 24, 2019 8:31 pm

scott1328 wrote:
romansh wrote:[Assuming the same "work" goes into ordering and shuffling?

That is a bad assumption.

Which one do you think has more work done?
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Re: Question on entropy

#47  Postby newolder » Jun 24, 2019 8:39 pm

Shuffling in the dark is easy; sorting into suit order needs the energy of illumination.

But we've already flogged this dead horse earlier in the topic and agreed that card pack order has little, if any, connection to entropy. :yawn:
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Re: Question on entropy

#48  Postby romansh » Jun 24, 2019 8:42 pm

newolder wrote:Shuffling in the dark is easy; sorting into suit order needs the energy of illumination.

But we've already flogged this dead horse earlier in the topic and agreed that card pack order has little, if any, connection to entropy. :yawn:

Agreed
cf Hack's
As for the deck of cards thing, in reality, an ordered deck has only slightly lower entropy than a shuffled one.
I agree with where Hack is going with this ... just clarifying the point.
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Re: Question on entropy

#49  Postby Spearthrower » Jun 24, 2019 11:46 pm

newolder wrote:Shuffling in the dark is easy; sorting into suit order needs the energy of illumination.

But we've already flogged this dead horse earlier in the topic and agreed that card pack order has little, if any, connection to entropy. :yawn:


Right, its connection is metaphorical, not factual. Card values don't possess any intrinsic energy property in order for them to bein a gradient; it's only values we assign that are completely independent of anything to do with any aspect of the card.

Metaphorically, there's only one way for a deck of cards to be ordered and - I can't do math so - shitloads of ways for it to be not ordered (according to the values we assign)... so in that metaphor, the ordered deck has the higher (maximal?) entropy, there is no other way for it to move from that state. Basically, it's the glass of ice and the glass of water metaphor.
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Re: Question on entropy

#50  Postby romansh » Jun 25, 2019 1:21 am

Spearthrower wrote: so in that metaphor, the ordered deck has the higher (maximal?) entropy, there is no other way for it to move from that state. Basically, it's the glass of ice and the glass of water metaphor.

This I think is perpetuating the metaphorical myth,

A pack of cards in of itself has an entropy whether sorted or random.

A system of a pack of cards and a shuffler or sorter also have an entropy. The sorter can do work and sort the cards and the system's entropy will increase. Or the shuffler can do work and shuffle the cards and the system's entropy will increase. We could argue, possibly quite accurately, that it takes more work to sort. But then the shuffler can continue shuffling until the same amount of work was done.

In what way will the entropy of the cards be lower for the sorted pack?
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Re: Question on entropy

#51  Postby Spearthrower » Jun 25, 2019 2:56 am

romansh wrote:
A pack of cards in of itself has an entropy whether sorted or random.


The pack of cards might as physical objects, but the values on the cards don't.


romansh wrote:A system of a pack of cards and a shuffler or sorter also have an entropy. The sorter can do work and sort the cards and the system's entropy will increase. Or the shuffler can do work and shuffle the cards and the system's entropy will increase. We could argue, possibly quite accurately, that it takes more work to sort. But then the shuffler can continue shuffling until the same amount of work was done.


Then it's nothing to do with the cards themselves because there's no actual system connected to them aside from a manufactured value - they could all be blank. It's the person who is performing some task that might have the quantity of entropy, not the cards' order or their values.


romansh wrote:In what way will the entropy of the cards be lower for the sorted pack?


As I said, there's a metaphorical idea here, but there's no actual entropy involved with the sorted or unsorted pack.

Ask it another way: what's the energy gradient inherent in the system of a deck of cards? Where's the disequilibrium?
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Re: Question on entropy

#52  Postby romansh » Jun 25, 2019 3:06 am

Spearthrower wrote:
Ask it another way: what's the energy gradient inherent in the system of a deck of cards? Where's the disequilibrium?

For the purposes of this discussion the "disequilibrium" is in the sorter and shuffler.
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Re: Question on entropy

#53  Postby Cito di Pense » Jun 25, 2019 3:49 am

romansh wrote:
Spearthrower wrote:
Ask it another way: what's the energy gradient inherent in the system of a deck of cards? Where's the disequilibrium?

For the purposes of this discussion the "disequilibrium" is in the sorter and shuffler.


And your point would be? It's already been mentioned that each sorting of the deck is equally probable. You're stuck on the notion that there is only one sorting that is 'ordered' according to the definitions of suit and rank, and that's completely arbitrary. Every other sorting of the deck is just a permutation of the order. To render it in the "balls and urns" formalism, there are 52 urns containing one ball each and no empty urns. The balls are distinguishable but the urns are not, unless the urns are labeled. In physical systems, energy levels are populated or they are not.
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Re: Question on entropy

#54  Postby hackenslash » Jun 25, 2019 8:01 am

Exactly right. As noted by Styer in the paper I quoted, disorder is a metaphor for entropy. Indeed, the deck of cards is a metaphor for a metaphor. It's a metametaphor. :lol:
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Re: Question on entropy

#55  Postby Spearthrower » Jun 25, 2019 10:04 am

romansh wrote:
Spearthrower wrote:
Ask it another way: what's the energy gradient inherent in the system of a deck of cards? Where's the disequilibrium?

For the purposes of this discussion the "disequilibrium" is in the sorter and shuffler.



Then, as I noted above, we're not just talking about the pack of cards anymore - the system isn't isolated. The shuffler's introducing energy, the shuffler gets their energy from eating, the food gets its energy from chemistry and sunlight and so on.

The thing about metaphors is that they're meant to help elucidate, and if you find they're obfuscating then they should be dropped immediately.

Recall, the idea you originally posed was a pack of cards arranged by suit and order or a shuffled pack, i.e. the action had already happened.
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Re: Question on entropy

#56  Postby Spearthrower » Jun 25, 2019 10:07 am

Cito di Pense wrote:
romansh wrote:
Spearthrower wrote:
Ask it another way: what's the energy gradient inherent in the system of a deck of cards? Where's the disequilibrium?

For the purposes of this discussion the "disequilibrium" is in the sorter and shuffler.


And your point would be? It's already been mentioned that each sorting of the deck is equally probable. You're stuck on the notion that there is only one sorting that is 'ordered' according to the definitions of suit and rank, and that's completely arbitrary. Every other sorting of the deck is just a permutation of the order. To render it in the "balls and urns" formalism, there are 52 urns containing one ball each and no empty urns. The balls are distinguishable but the urns are not, unless the urns are labeled. In physical systems, energy levels are populated or they are not.



Yep, a directed outcome; the 'ordered' deck being suits and numbers according to an essentially arbitrary system of symbols of human shorthand.
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Re: Question on entropy

#57  Postby Spearthrower » Jun 25, 2019 10:08 am

hackenslash wrote:Exactly right. As noted by Styer in the paper I quoted, disorder is a metaphor for entropy. Indeed, the deck of cards is a metaphor for a metaphor. It's a metametaphor. :lol:


:grin:

So glad you're here! :grin:
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Re: Question on entropy

#58  Postby Blip » Jun 27, 2019 9:24 am

Thank you both (all) for the explanations. I've completed the course successfully, by the way, and this was the most difficult idea for me to grasp, not least because my preconceptions got in the way.
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