131–140 of 144 posts
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I don't think that's true. An object would be attracted to the inner surface of the sphere because that's where the mass actually is. The shape you're describing doesn't have a center of mass the way we traditionally think of it.
At the center of a uniform hollow sphere the force will be precisely 0.
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> aren't people (and all living organisms) the quintessential example of a local decrease in entropy that results in greater overall entropy Complexity is orthogonal to entropy. The aforementioned barrier-separated box is high in entropy but simple. Upon lifting the barrier, a description of the gas front moving into the vacuum is enormously complex. It is also lower in entropy than the previous, barrier-separated st…
Is there a way to quantify complexity in that sense?
So this article does the Maxwell Demon some injustice. There is a key point about the demon that when he is 'sorting' the particles into two bulbs or rooms, that the gate he is working on is frictionless. In this way, you can can see that there is no energy entering the system, yet the entropy is decreasing. Now, this is where things get interesting to me (please correct me if I'm wrong here). What the demon is addin…
I think that was Schrodinger's argument in "What is Life": nature seeks to maximise entropy, and life does a very good job of it.
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I don't think so. There is no energy transmission involved at all. I suspect that there is some entropy transmission, but I didn't see an analysis of that, and the amount is negligible compared to what is already in the quantum mechanical system. Of much greater surprise to me was the claim that an isolated quantum mechanical system neither gains nor loses entropy. I'm almost as astonished at this as I am at the fact…
> Of much greater surprise to me was the claim that an isolated quantum mechanical system neither gains nor loses entropy. Why is this surprising? It's a simple consequence of unitarity.
So this article does the Maxwell Demon some injustice. There is a key point about the demon that when he is 'sorting' the particles into two bulbs or rooms, that the gate he is working on is frictionless. In this way, you can can see that there is no energy entering the system, yet the entropy is decreasing. Now, this is where things get interesting to me (please correct me if I'm wrong here). What the demon is addin…
> There is a key point about the demon that when he is 'sorting' the particles into two bulbs or rooms, that the gate he is working on is frictionless. Exactly. Maxwell's Demon is a magical construct. In reality, any active device that sorts molecules into high and low energy bins would take power to run, and would generate more heat (or other entropy) than it removed by doing the sorting.
Edit: I think you might be speaking to my point that in the end it evens out, and that natural selection in turn does create entropy even as its generating information.
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aren't people (and all living organisms) the quintessential example of a local decrease in entropy that results in greater overall entropy? we are highly ordered groupings of matter but we're really great at churning about the matter and energy around us and we eventually decompose too.
A living organism is of course a noble endeavor standing against the tide of entropy. But it can do so only with significant influx of energy extracted from its external environment. The cost of constructing such an elaborate order of matter is paid by disorder elsewhere. As we know, the living stance can be maintained for only a relatively short time, after which it rapidly decomposes to background entropy. Interest…
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> Of much greater surprise to me was the claim that an isolated quantum mechanical system neither gains nor loses entropy. Why is this surprising? It's a simple consequence of unitarity.
It surprises me because the universe is an isolated quantum mechanical system that certainly appears to be gaining entropy.
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Would you mind sharing a link to a proof of the second law using Markov chains and information theory? I'd like to learn more about this approach. I'm surprised that Markov chains would be involved when the laws of physics are deterministic. The Poincare recurrence theorem has always suggested to me that the second law is not as fundamental as other laws. For a finite system with finite phase space, the state of a sy…
I am on mobile now, and can't provide a simple link, but it is given in Cover&Thomas "Elements of Information Theory", in the episode that discusses entropy of markov processes. I can find pages in google books but they won't zoom big enough to read... IIRC, the proof requires the markov chain be irreducible, and extends to the general case by summing over the irreducible parts; and that entropy will stay the same or…
[0] staff.ustc.edu.cn/~cgong821 /Wiley.Interscience.Elements.of.Information.Theory.Jul.2006.eBook-DDU.pdf seems to have a copy indexed by Google. I suspect it is not legitimate
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The second law of thermodynamics is as fundamental as the uncertainty principle: The former is a result from markov chains and information theory, the latter is a result from fourier analysis of conjugate variables. What would you consider a "fundamental physical law"?
The uncertainty principle is an absolute and inviolable consequence of pure mathematics; the second law of thermodynamics just makes predictions that are "very very overwhelmingly likely". The probability of the application of the uncertainty principle producing an incorrect prediction (internal to the theory) is zero, whereas the probability of the application of the second law producing an incorrect prediction (aga…
I did not remember the exact statement when I posted earlier, but here it is: the statement of the (markov) 2nd law of thermodynamics is also a statement about the sample space: It says that in expectation (over the ensemble) the relative entropy decreases towards that of stationary distribution (which in most systems is the highest entropy distribution possible in that system, thus absolute entropy is non decreasing). That is, unless the system starts at a state with a higher entropy than that of the stationary distribution, entropy will not decrease.
Both are mathematical statements, consequences of pure mathematics, neither of which gives a prediction - they both give ensemble averages, and both are both internally perfectly correct and consistent. See Cover & Thomas, 2nd Edition, Jul 2006, pg 81, section 4.4 - entropy rate of markov processes. Unless, of course, you are referring to a different version of the uncertainty principle which I am not familiar with.