Darby,
If we take a volume of space and infuse it with a gas and compact ourselves so that we are small enough to actually see the individual molecules of the gas (disregarding the real physics involved in doing this) all we see is a chaotic world. It is totally ruled by chaos and quantum uncertainty. Yet if we back away and go back to our "real" perspective of the world around us we see order and, at least to some extent, predictable outcomes for the system.
I don't know if I have ever read such an excellent and compact description of both classical and statistical thermodynamics, and what they mean to our human perception, as you have offered here. Very well done, sir.
In one domain we perceive things as chaotic, non-linear, quantum, or statistical. It is no coincidence that the mathematics of statistics & probabiliy helps us greatly in understanding what we are perceiving non-linearly. (perhaps subconsciously)
In the other domain we perceive things as ordered, linear, deterministic, or directly-predictable. It is no coincidence that a "classically Newtonian" set of mathematics (i.e. calculus of variations) can accurately model these, our linear perceptions of our universe.
Clearly, these two views of physics are complementary. Together they represent the "+" and "-" poles of just another polar(+/-) variable (i.e. thermodynamic state). Any resolution of polar opposite energies always define a "surface interface" (3-D? 4-D?) between those two polar field effects.
Is it possible, perhaps, that "where we live" is defined by this interface? I like to call this interface "The Integrated Matrix of Massive Space-Time." Gets me thinking about many things... Thanks again, Darby.
RMT