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Why should entropy depend on the observer?I have often heard people say "entropy depends on the observer."
Well, that definition of entropy is a little circular, because ##T## is in turn defined via ##1/T = \frac{\partial S}{\partial U}|_{V}##.Why should entropy depend on the observer?
"The entropy of a substance, its entropy change from 0 K to any T, is a measure of the energy that can be dispersed within the substance at T: integration from 0 K to T of ∫Cp/T dT (+ q/T for any phase change)." (Frank L. Lambert, "Entropy Is Simple, Qualitatively", J. Chem. Educ., 2002, 79 (10), p 1241)
The question is: how is ##T## defined?Entropy is linked to energy through its original definition by Clausius, dS = dQ/T, where "d" connotes a very small change.
Point taken, but there's another issue even after you've chosen the macroscopic variables. Given macroscopic variables ##E, V, N## (total energy, volume and number of particles), there are many (infinitely many in the classical case, and astronomically many in the quantum case) microstates consistent with that macrostate. But are they all equally likely? If not, what's the probability distribution?The question is: Does entropy depend on the observer?
When transfering a system from state 0 to state 1 (both characterized by a set of selected macroscopic observables), you can in principle think of any reversible process to define the entropy in state 1:
S1 = S0 + ∫δQrev/T (integration from 0 to 1)
The "subjective" part is merely the definition of the macroscopic observables you want to keep track of for the given system (temperature, pressure, volume, number of particles etc.).