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Last night I was reflecting on what I wrote and realized an egregious mix-up
occured.
the section that read
The statistical underpinnings of the 2nd law of thermodynamics do not implythat the >entropy of an isolated system increases or stays the same for any
given process. It is >possible for an isolated system, through spontaneous
fluctuations, to have a lowering >of its entropy.
and below has a serious confusion. Everywhere where I refer to an isolated
system, I should have said a system held at constant temperature by means of
being in thermal contact with a reservoir at that temperature.
i.e. I was thinking in terms of a canonical ensemble, but wrote a
description of a system best interpreted in terms of a micro-canonical
ensemble.