Russell Standish wrote:

>Also note that exact measurements of microstates is *in principle*
>incompatible with the Heisenberg Uncertainty Principle.

Well, that's why I defined microstates as "detailed descriptions of the 
positions and momenta of all the particles, within the limits of the 
uncertainty principle". My memory is that in the quantum version of 
statistical mechanics, the phase space is partititioned into finite regions 
so that the uncertainty principle does not prevent you from measuring which 
region the system is in (and the regions are made as small as possible while 
still having that be true). I wonder if there'd be a natural way to look at 
statistical mechanics in the MWI interpretation though--I would think the 
maximal information about a system, analogous to the "microstate", would be 
the system's exact quantum state (which only assigns amplitudes to different 
values of noncommuting variables like position and momentum), and the 
evolution of the system's quantum state over time should be completely 
deterministic, and also "information-preserving" in the sense that knowing 
the quantum state at a later time would tell you the quantum state at an 
earlier time. But I can't think what "macrostates" you'd use, since a 
particular quantum state can involve a superposition of different possible 
temperatures, pressures and so forth.


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