My book uses the argument that the multiplicities of a few macrostates in a macroscopic object take up an extraordinarily large share of all possible microstates, such that even over the entire lifetime of the universe, if each microstate had an equal chance of being accessed, fluctuations away from equilibrium would never occur.
My question to this statistical proof is this: In the real world, is there really an infinitesimal but nonzero chance that macroscopic systems could access some of the more unlikely macrostates (e.g. heat transfer from a cold object to a hot object)?
Answer
I guess so - I mean, as far as I know, there's no law of physics that strictly prohibits those "exotic" states from being realized. As long as the state exists and can be reached by some path from the "center" of the state space where the likely states are, there should be a nonzero (not even infinitesimal, really) probability of accessing it. But for a typical system, that probability is really, really, really small. So small that it's impossible to intuitively comprehend just how unlikely such an event is.
The thing is, a lot of people aren't used to dealing with even moderately large or small numbers. If you confront them with a probability like $10^{-10^{23}}$, they often fail to put the smallness of that value in perspective, and instead focus on the fact that it's not strictly equal to zero. From there they may start coming up with all sorts of nonsensical ideas about walking through walls and spontaneous combustion (the weird kind) and the like. So physicists usually find it easier to just say the probability is zero - and in fact, for any purpose other than a rigorous mathematical proof, it might as well be.
(Sorry about the rant, I know most people are actually relatively sensible about these things, but it bothers me that the crazy ones seem to get all the attention despite being wrong.)
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