dheddle
Posts: 545
Joined: Sep. 2007
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On the topic of entropy--a question.
Do you think only the difference in entropy has physical significance? I've been thinking a great deal about this. The conventional answer is "yes" (I once argued about this Mark Perakh on PT and he dismissed me out of hand—arrogant bastard—I don’t mind being dissed by superstar physicists but not garden-variety physicists—but I digress.)
I’m teaching thermo and have been thinking about this a great deal. Of course, all the equations involving entropy can be cast in terms of the difference in entropy—but that’s not exactly what I am asking. (For example, we can add a constant momentum to everything, and Newton’s 2nd Law still applies, but we don’t go about carefully stating that only changes in momentum are relevant.)
I’m thinking, of course, of the quantum basis for entropy—which unlike the classical basis is not mysterious at all. Every microstate (because of Heisenberg) has a finite volume in phase space, therefore we only have a finite (though typically ginormous) number of microstates for each macrostate. That is certainly a well defined absolute quantity: the number of macrostates. It is a positive definite integer. In order to free ourselves from dealing with enormous numbers—numbers with exponents in the exponents, we shrink ‘em down—and make them additive rather multiplicative by taking the log—and give that quantity the name entropy. Nothing mysterious.
The number of microstates is clearly a well defined quantity—so why not the entropy, which is just a smoothing thereof? We define absolute zero and an absolute temperature scale—as if temperature has some absolute meaning—but in fact all those formulae that demand that you insert an absolute temperature can be recast in terms of a temperature difference. And entropy is more fundamental than temperature.
Anyway, I think the language is simply a carryover from classical thermodynamics. And I think it is wrong—I think it at least makes a certain sense to say that S=0 when the number of microstates = 1, and that this is not arbitrary in the same sense that the zero of a potential energy is arbitrary.
If Louis cares to chime in he may not use enthalpy. The friggin' chemists and their friggin' enthalpy really piss me off!
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Mysticism is a rational enterprise. Religion is not. The mystic has recognized something about the nature of consciousness prior to thought, and this recognition is susceptible to rational discussion. The mystic has reason for what he believes, and these reasons are empirical. --Sam Harris
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