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Feb28-12, 06:20 PM
P: 1,583
Quote Quote by Ken G View Post
No, that is exactly what cannot be true, in any theory of mechanics exhibited by large systems. That's pretty much the whole point of thermodynamics! Again, "disorder" simply means "more ways of being", which means "more likely", and that's the second law in a nutshell. The sole assumption is that you can just count the ways of being (the number of configurations)-- this is the crux of statistical mechanics, that every individual state is equally likely. That's the only assumption behind the second law, and if it weren't true, it would only mean that we would need to have a more sophisticated concept of what entropy is, beyond just ln(N).
Are you saying that it is literally impossible to have laws of physics in which all the particles work together to produce a particular ordered state?
And that is what is not true. Newton's laws are about the details, thermodynamics is what you can do without anything like Newton's laws. That's why the main principles of thermodynamics were discovered independently of Newton's laws (like the work of Carnot and Clausius), and sometimes even prior to them (like Boyle's law).
Sure, just like Kepler's laws were discovered before Newton's law of gravitation and the Balmer series was discovered before the Schrodinger's equation. Phenomena of nature can be discovered independently even if they derive theoretically from a common source.
Right, with no reference to any mechanism or mechanics of the Demon. This is crucial-- the mechanics only serve as informative examples of the second law, they are not part of the derivation of it. The derivation proceeds along the lines I gave above, and with no mention of any laws of mechanics.
I was envisioning a different sort of procedure. I'm suggesting doing the statistical mechanics derivation of the second law of thermodynamics from Newton's laws of motion, as outlined in the Feynman lectures and fleshed out by Boltzmann, but restricting the proof to the case where you have a Maxwell's demon with unspecified mechanism. So the rest of the scenario will be analyzed according to mechanics, it is only the demon that is a black box.
If you set F=mv instead of ma, as the ancients imagined, you still get the second law of thermodynamics, without any difference. Indeed, this is the second law in highly dissipative situations, and it's still just thermodynamics.
I don't think this is too surprising; (this part of) Aristotelian physics is just Newtonian physics in the limit of strongly dissipative forces.