What does it even mean to “completely describe” a gram of water
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That takes a physics course to explain, but here's the basic idea. The molecules in water are wiggling around... it takes a lot of information to say exactly what they're doing at any moment ... but thanks to quantum mechanics, it's only a finite amount of information!
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Wouldn't you want the relative entropy of the proposed configuration that encodes information relative to the equilibrium/minimum entropy configuration under the relevant temperature, volume, mass, boundary, etc, conditions?
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I'm a bit confused here since equilibrium is given by maximizing entropy with respect to the constraints, not minimizing it.
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More interesting than the number of bits per gram is the number of bits per molecule: about 7.1
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@ScottCentoni - I'm getting 12.13 bits per molecule - closed to what you said, but not the same. I'm not sure what's up. You can see my calculation here: http://math.ucr.edu/home/baez/information.html#water … - Još 5 drugih odgovora
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Also, how is this calculated, is it some kind of combinatorial degeneracy based on moving atoms around, or is it the Bekenstein bound?
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The entropy of water at room temperature and pressure is *measured* to be 3.88 joules/kelvin per gram. To convert entropy to bits of information, divide by Boltzmann's constant and ln(2). This all comes from Boltzmann and Shannon. (1/2)
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Holographic principle implies one can store 10exp123 bits in the Universe (actually at the cosmic horizon, if I am not wrong). Seth Lloyd has written a paper on the computational capacity of the Universe (a different topic):https://youtu.be/XxVlGAFX7vA
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I computed the maximum possible information that could be stored in the so-called "observable universe" - which should probably be called the "formerly observable universe": http://math.ucr.edu/home/baez/information.html#universe … I got 10^124 bits, but what's an order of magnitude among friends?

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