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Author Topic: How much energy must be expended to sort a set?  (Read 2984 times)

Offline Atomic-S

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How much energy must be expended to sort a set?
« on: 18/12/2008 04:46:18 »
We know that to sort a mixture of gasses into separate compartments the sum of whose volumes is equal to the original volume, a certain minimum work must be done, pursuant to the Second Law of Thermodynamics. If this is so, does it imply that to do any sorting operation, there exists an irreduceable minimum energy that must be expended? In other words, no computer could be constructed that would sort a list alphabetically which would not consume an irreduceable minimum of energy.


 

Offline Supercryptid

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How much energy must be expended to sort a set?
« Reply #1 on: 18/12/2008 09:48:28 »
If you waited long enough, a pair of boxes (Box A and Box B) linked by a pipe containing a mixture of two gases would eventually sort itself. Probability insists on it. If we consider the gas molecules to be moving randomly and to end up in either box at random times, then a time in the very distant future must come when all of the molecules of Gas A would be in Box A and all of the molecules of Gas B would be in Box B. This would be a very fleeting state and would quickly rediffuse all over again. You'd probably have to wait like 10^100^100^100... years or some crazy number like that before the gas molecules returned to their original, sorted stated. Therefore, the minimum energy required to sort the gas is technically zero (zero energy input into the system from outside, anyway).
 

Offline LeeE

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How much energy must be expended to sort a set?
« Reply #2 on: 19/12/2008 01:02:34 »
I believe that for a perfect sort the amount of 'energy' is irreduceable.  Less accurate sorts can use less energy - it depends on how accurate a sort is required against your energy budget.  If the energy budget is what is driving things then a drunkard's walk type algorithm has the potential to produce high quality results, but don't bet on it being right.  If the results are of utmost importance then you need to spend the energy.
 

Offline Atomic-S

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How much energy must be expended to sort a set?
« Reply #3 on: 19/12/2008 07:28:35 »
Quote
a time in the very distant future must come when all of the molecules of Gas A would be in Box A and all of the molecules of Gas B would be in Box B. This would be a very fleeting state and would quickly rediffuse all over again.
Perhaps I should have been more specific: I would be referring to the situation in which the set was sorted usefully, that is to say, observably. If chance is to be relied upon to do the sorting, there must be some way of recognizing when the task has been accomplished, so that a valve between the compartment can then be slammed shut and the results made usable.
 

Offline Soul Surfer

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How much energy must be expended to sort a set?
« Reply #4 on: 19/12/2008 23:03:42 »
Yes there is a minimum energy but to achieve it you would have to use a computing engine that used the thermodynamically minimum possible energy for processing and no machine ever does this by a very large margin there are also problems about how you define your processer and you would probably have to use quantum computation.

It is an interesting question.

to return to the sorting molecules problem.  This minimum energy is of very great practical importance in many chemical processes notably the desalination of seawater
 

Offline Mr. Scientist

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How much energy must be expended to sort a set?
« Reply #5 on: 24/12/2008 20:04:26 »
We know that to sort a mixture of gasses into separate compartments the sum of whose volumes is equal to the original volume, a certain minimum work must be done, pursuant to the Second Law of Thermodynamics. If this is so, does it imply that to do any sorting operation, there exists an irreduceable minimum energy that must be expended? In other words, no computer could be constructed that would sort a list alphabetically which would not consume an irreduceable minimum of energy.

No.

Let's just clarify, what you heard, but....

''We know that to sort a mixture of gasses into separate compartments the sum of whose volumes is equal to the original volume,''

Is the law of conservation, and...

''a certain minimum work must be done,''

Is also known as the principle of least action. It comes from Langrangian Mathematics, which i would rather not display, unless asked on request. It says that the motion of matter, in fact, all lightspeed, maybe possible tachyon speeds, and even bradyonic speeds, such as protons and neutrons, all happens under the least amount of energy from what is available. The absolute value of energy, cannot be known for sure, however, there is some speculation as to whether it may arise from an infinite negative sea of energy embedded in the vacuum.

This has a description very similar to The Cosmological Constant, The Microwave Background and even the Zero-Point Energy Field: Some have even postulated they may all be related. However, you also say later:

'' there exists an irreduceable minimum energy that must be expended?''

No, it's not irreduceable. At the level of electrons and quarks, forward operation and backwards operation are in equal favor, according to theory. They really don't have a cause or experience an effect, so they are free from these superior observatory attributes.

The energy is not irreducable, unless there is a symmetry in time itself. As weird as this sounds, this is just another way to express the big crunch theory, where gravity is dense enoughm radiating enough gravitational waves to cling to the very expansion of the universe, spanning it's wide radius at the speed of light, when it finally stops on itself, and reverts back to the state in exactly the way it began it's original state, (in absolutely the same way it arrived, it went back in exactly the same way), because of the principle of least action. Matter in this idea, tends to be stable in its used of energy... under the right conditions.

 

Offline yor_on

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How much energy must be expended to sort a set?
« Reply #6 on: 25/12/2008 11:05:18 »
"At the level of electrons and quarks, forward operation and backwards operation are in equal favor, according to theory. They really don't have a cause or experience an effect, so they are free from these superior observatory attributes."
Are you talking Feynman here?
And using his definitions to explain why there is a 'no loss' of energy.

And explaining the BB or crunch too?
It makes good sense although in a weird way.
I can see how one might see that in a 'closed system' nothing can be lost.
But when 'transformed' into that final 'soup' it has lost something yet, hasn't it.
Its capacity to further transformations.

So 'something' seems changed.
But looked at the way you might mean, makes it both stranger and simpler.
Somehow it seems to mean that what we see as 'energy' when broken down to its smallest constituents won't care for times arrow any more.

Even though 'time' still will be 'there' as some kind of conjugation.
As one expression of spacetime, but at this 'size' matter seems to lose its consistency.

Am I making sense here.
Probably not, but I'll write it anyway.

 

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How much energy must be expended to sort a set?
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