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Gyan,
It's true that we could be "wrong"--or at least disagree with one another--about how to identify and arrange microstates. I can think of three possible ways; none of these really pose a problem in terms of "subjectivity," though.
1) We could choose to classify microstates differently, by defining our macrostates with reference to a new set of properties. For instance, we could define the macrostates of a gas not with reference to temperature and pressure, but with reference to the first nth Fourier components of the density and velocity distributions.
This would give us a new set of macrostates, and entropic considerations would give us a new set of predictions about the system's thermodynamics. These would not contradict our old predictions, because those were made about a differently-defined set of macrostates. In fact, both sets of predictions together give us more information about the system than either set alone. So "imposing a new organizational schema" in this sense simply lets us work the thermodynamic equations for all they're worth.
2) There could be more microstates than we realize, because of some unknown degree of freedom (e.g. "spin" or "color") which is independent of the known ones. For instance, in a free-electron gas we might be defining microstates by electron position and velocity (or their quantum equivalents), but not by spin.
This would not affect entropic considerations, because the entropy of a macrostate is a function of the logarithm of the number of microstates. An independent degree of freedom would simply multiply the number of microstates in each macrostate by a constant--which would raise the entropy of each macrostate by a constant. Since the system's behavior only depends on the entropy of one macrostate relative to another,, our predictions would not change.
3) There could be an unknown degree of freedom which is not independent of the known ones--or, equivalently, a degree of freedom we believe in might not actually exist. This would change the number of microstates per macrostate by a non-constant factor, so that the relative entropies of macrostates would be different.
This would change our predictions. And that gives us a way to test them! If a system evolves in a way such that entropy seems to increase, our assumptions about its possible microstates must be wrong. Experiments on this issue can advance our understanding of a system by suggesting new degrees of freedom, or new ways that known degrees of freedom might correlate. In this case, observed experimental results will tell us whether our "subjective" microstate arrangement method is right or wrong.
Are you thinking of instances of subjectivity which lie outside these three categories? If so, could you outline them? |
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