Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Atomic-S on 16/04/2015 06:56:05
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The Second Law of Thermodynamics says that in any process, the entropy of the system plus its environment cannot decrease. That says that the entropy of the system can decrease if that of the environmnent increases by an equal or greater amount, and of course, the phenomenon is demonstrated all the time, as in the isothermal compression of a gas. What is less than clear, however, is whether the entropy of the system can decrease during a time in which it is isolated from its environment. The challenge thus is to do the following: do an experiment in which a system and its environment are allowed, if applicable, to interact initially, being set upon a course in which there is, as time passes, a net overall increase in entropy The direction of the entropy of the system itself during this time interval could be anything, but we might speculate that it starts off heading downward. Then the system is isolated from its environment for a certain additional time interval (such as by enclosing it in an evacuated idealized reflective shroud perhaps made of a superconductor), during which time the system decreases in entropy while its environment increases in entropy by at least the same amount, and then when the container is opened again, the system is found to be in a lower state of entropy than when it was put in. Meaning that, as far as the system is concerned, it lost entropy while disconnected from the rest of the universe, thereby becoming a "mini-universe" in which entropy was running backward. That seems to be consistent, in principle, with the Second Law because its loss of entropy was offset by the gain in entropy elsewhere; but is there any way to do it in practice?
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The second law of thermodynamics is just a result of the statistics of large collections of small particles. It is not impossible for a system to spontaneously "lose" entropy, just highly unlikely. The probability that the entropy decreases at a given instant increases when there are only a few particles that can only occupy a few states.
Consider a system that contains three identical particles that can each be in either of two states (A or B). For ease of consideration, let us say that both states have equal energy, and nothing prevents the interconversion of states.
The system can adopt any of four distinguishable states (1: 3 particles in state A, 2: 2 particles in state A, 3: 1 particle in state A, and 4: 0 particles in state A), but the states that include particles in both A and B states are degenerate, so there are a total of 8 possible states, but only 4 can be distinguished:
1: AAA
2: AAB ABA BAA
3: ABB BAB BBA
4: BBB
Therefore system states 2 and 3 have greater entropy than either 1 or 4. At any given instant, the system is more likely to be in one of the mixed (high entropy) states than one of the pure (low entropy states). However, when the system is in either of the high entropy states, the particles don't stop switching between A and B. A system in state 2 is twice as likely to change to state 3 as state 1 (if only one particle can switch at a time--there are two A-particles each of which could switch to a B-particle, and only one B that could switch to A).
But this means that the system could (and would) spontaneously change from state 2 to state 1 with a loss of entropy.
If we consider a system with 100 particles, the "pure" (lowest entropy) states are much harder to come by, but a system with maximal entropy is still likely to deviate slightly and transiently. Once we consider macroscopic systems (>1010 particles) the high entropy states will be completely dominant, but there will still necessarily be some transient loss of entropy.
Overall, the reason that the 2nd law of thermodynamics appears to hold true in essentially every experimental case is twofold: any system we experiment with usually contains incredible number of particles, and usually starts in a relatively low state of entropy (the universe overall has an ungodly number of particles, and appears to have started in or previously attained a state of very low entropy.)
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Sweet thinking Chiral. Now, define the difference between entropy and a local arrow.
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Entropy is just S = kB*log(W) where kB is Boltzmann's constant and W is the number of microstates in the system.
The local arrow is a concept that I am less familiar with, but I will do my best. I think the local arrow defines the order in which states are determined. The principle of microscopic reversibility says that if it is possible to convert (macro) state A into state B, then it must be possible to convert state B into state A (but not necessarily just as easily). This only applies when one state is directly converted to another (instantaneous timescale). On longer timescales (such as our macroscopic experience, or even using ultrafast femtosecond detection methods) there are usually several intervening states, so the path A→Z→Y→X→W→V→U→S....→B is *highly* unlikely to reverse, even though it is, in principle, possible (it would be like two friends accidentally picking the same 100-digit lottery number randomly).
What the "cause" of this arrow is, I have no clue...
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:)
Ahh, not sure I will agree there. Entropy is something able to reverse, sometimes, as you say, but when you find it doing so it does it inside your local arrow, as defined by your wristwatch. So any experiment you enact proving the first concept, will use that arrow, having only one direction (macroscopically defined). That is if we use a experiment to test it. I see no way for a arrow to reverse, even though it can be defined to 'stop', as when defining a far away clock 'rate' (for example a event horizon), compared to my own local definition. In fact, it doesn't locally 'stop' then too, as that is the clock you use to define all others against. There is a truth to what you say, and I too think the arrow must be a construction of some sort, but the principle for ones local arrow has to be something different than a equivalence to microscopic states of a 'system'
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You misunderstand me--I do not think that the states determine the arrow, or that entropy determines the arrow, or anything like that. The local arrow is defined by something else--it is only the successive evolution of states that allows us to observe the direction of time. As time progresses the universe changes in predictable ways, but those changes do not drive time, they are a result of it.
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As time progresses the universe changes in predictable ways, but those changes do not drive time, they are a result of it.
You seem to be saying that change is the result of time. Isn't that a bit like saying that the object I measure with a ruler is a result of the ruler? Isn't time just the concept we use to measure change?
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Allow a small drop of red ink to be placed in gal. of water and watch what happens. As the mixture seeks an equilibrium and order turns into disorder, the red drop of ink will become completely diluted within the water. This is entropy in action and the measure of time this event takes defines the duration of this arrow that yor_on is talking about. Can it be reversed? According to special relativity, it can but the probability of such an event occurring is highly unlikely.
Will that red drop of ink reconstruct itself into that individual drop after being completely dispersed within that gal. of water? The probabilities of that happening are so slim, the math involved is almost beyond reason.
It's the probability of such an event reversing that proves, to we the observer, that such an event is so close to ZERO that we can invest our trust in this arrow, this arrow we call time. And the law of probabilities is what gives the arrow it's direction.
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If you are very careful, you can get that frop of dye to reassemble:
Laminar flow is very cool!
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If you are very careful, you can get that frop of dye to reassemble:
Laminar flow is very cool!
But of course we can, through our manipulation. All we need to do now is figure out how much we've contributed to overall Entropy as a result of our manipulation. Add up both results and Entropy still wins the contest.
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Yes, entropy always wins. It's just a cool video...
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You misunderstand me--I do not think that the states determine the arrow, or that entropy determines the arrow, or anything like that. The local arrow is defined by something else--it is only the successive evolution of states that allows us to observe the direction of time. As time progresses the universe changes in predictable ways, but those changes do not drive time, they are a result of it.
good to know Chiral :) I'm starting to become a great fan myself, of the 'coexistence of stuff', which also can be translated to symmetries as I think, or 'everythings dependence on everything' (Mach principle in a way). Or even possibly the idea of decoherence? If you imagine it as a whole description of what a 'universal container' should mean? Although that one is far fetched.
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The Second Law of Thermodynamics says that in any process, the entropy of the system plus its environment cannot decrease.
That's not quite true. Entropy is based on probability. So its extremely likely that the entropy will always increase but its not a mathematical certainty that it can't reverse for a moment. It's just unlikely in the extreme.
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Yes, entropy always wins. It's just a cool video...
I agree chiralSPO, very cool video indeed.
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Definitely a cool video. Never saw that done before.