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The question of what are the states to count and how is not obvious. “It cannot be emphasized strongly enough that W is not the measure of the set C of all sta

by kgwgk 4y ago

The question of what are the states to count and how is not obvious. “It cannot be emphasized strongly enough that W is not the measure of the set C of all states […] compatible with the external macroscopic constraints; rather, it is the dimension of the subset of those states that can be realized in the greatest number of ways.” [Entropy and the Time Evolution of Macroscopic Systems, Walter T. Grandy Jr.]

deleted 4y ago
[deleted]
lisper 4y ago
That's interesting, I didn't know that. I always thought that W in k ln(W) was the number of possible states. Thanks for bringing this to my attention! I wonder, though, does this actually matter to anyone but a physicist? Consider the common just-so story about electromagnetic waves: a changing electric field produces a magnetic field, and a changing magnetic field produces an electric field. Therefore, once you start to wiggle an electron around, the changing field become self-sustaining and you end up with a wave. This story is wrong because it would lead you to conclude that the E and B fields are 90 degrees out of phase when in fact they are in phase, and understanding why that is requires going into quite a bit more detail. But does that actually matter to anyone other than a physicist or an antenna engineer?
- kgwgk 4y ago
  > I always thought that W in k ln(W) was the number of possible states. That formula - Boltzmann's entropy - is only applicable when all the microstates are equiprobable. The question of what does it mean in general is subtle. If we have a gas in a container in thermal equilibrium with a heatbath, for example, the energy of the microstates compatible with those constraints is not fixed and their probability depends on the energy. The energy and the pressure fluctuate. > I wonder, though, does this actually matter to anyone but a physicist? The people most concerned with the question of entropy on a conceptual level tend to be physicists - and philosophers. https://deepblue.lib.umich.edu/bitstream/handle/2027.42/43415/11098_2004_Article_207174.pdf https://deepblue.lib.umich.edu/bitstream/handle/2027.42/4341...

by kgwgk 4y ago

deleted 4y ago

[deleted]

lisper 4y ago

That's interesting, I didn't know that. I always thought that W in k ln(W) was the number of possible states. Thanks for bringing this to my attention! I wonder, though, does this actually matter to anyone but a physicist? Consider the common just-so story about electromagnetic waves: a changing electric field produces a magnetic field, and a changing magnetic field produces an electric field. Therefore, once you start to wiggle an electron around, the changing field become self-sustaining and you end up with a wave. This story is wrong because it would lead you to conclude that the E and B fields are 90 degrees out of phase when in fact they are in phase, and understanding why that is requires going into quite a bit more detail. But does that actually matter to anyone other than a physicist or an antenna engineer?

kgwgk 4y ago
> I always thought that W in k ln(W) was the number of possible states. That formula - Boltzmann's entropy - is only applicable when all the microstates are equiprobable. The question of what does it mean in general is subtle. If we have a gas in a container in thermal equilibrium with a heatbath, for example, the energy of the microstates compatible with those constraints is not fixed and their probability depends on the energy. The energy and the pressure fluctuate. > I wonder, though, does this actually matter to anyone but a physicist? The people most concerned with the question of entropy on a conceptual level tend to be physicists - and philosophers. https://deepblue.lib.umich.edu/bitstream/handle/2027.42/43415/11098_2004_Article_207174.pdf https://deepblue.lib.umich.edu/bitstream/handle/2027.42/4341...