and I suppose the "largeness" of the system is defined statistically?
I thought the topic of this thread concerned the validity
of the 2nd law. Since we have no reason to believe the
2nd law is violated on any size scale, large or small, we
have no need to define "largeness" or "smallness" ... not
statistically or otherwise.
Here is how I think of the 2nd law. If you don't set the
alarm clock, it doesn't know what time it is ... and the
clock can't figure it out on its own unless some information
flows across the boundary. http://www.av8n.com/physics/clock.htm
To me this is the essence of the 2nd law. You can't make
information out of no-information. This was obvious to me
when I was seven years old, and it has only become more clear
since then.
Does anybody think we can evade the strictures of the 2nd law
by building things on a "microscopic scale"? Would really tiny
clocks be able to set themselves??? I don't think so!
Would a really tiny telescope be able to violate the brightness
theorem, even temporarily? Sure, there will be fluctuations,
but there would be the same fluctuations if you aimed your detector
at the heat-bath *without* the telescope, so the telescope
hasn't accomplished anything.
For starters, read Feynman's chapter on "Ratchet and Pawl".
Sometimes the ratchet goes backwards, but that is not a
violation of the 2nd law ... indeed we would have a violation
if it didn't go backwards sometimes.
Try designing a Szilard engine or other Maxwell-demon device.
Try designing a NAND gate for a reversible computer.
Try designing a telescope that exceeds the limits of the
brightness theorem.
Try designing a self-setting clock.
Seriously, please try it. See where the problems arise. It
will give you some appreciation for conservation of phase space
and for the 2nd law in general.