Thanks for the suggestion from RTR. I had no idea it had an entire chapter on this stuff. I'm currently working on it. I'm stuck on the phase-space argument; the one concerning the gas filled in a small cavity with a valve, in a larger box, and then the valve is opened to let the air out in the larger volume of the entire box. I think I'm having linguistic problems since English is not my first language. Does the argument end with an explanation of how the entropy still really increases in the reverse direction but we have to take into account a much larger phase space or is the problem left unresolved? I'm talking about the last part of section 27.5, that is, pages 668 and most of 669. The writer's wording is a little confusing for me. Does he mean to say that taking into account the much larger phase space, including the entire solar system, the entropy increases even in the reverse time direction? If so, please explain his arguments here.
How is spontaneous emission reconciled with time reversal symmetry? Even statistically? Please do explain this. The wiki page you mentioned says nothing about reversibility of the phenomenon. In fact, if the process is reversible, as you say, then it really doesn't relate to the problem at hand since reversible processes are already consistent with time symmetry. It's the irreversible processes that have a problem with this symmetry.
I miss the point of this completely. Maybe you can dumb it down further to help me understand this :( I gave Maxwell's demon as an example to illustrate that no matter how simple a system is, you cannot really decrease its entropy over a significant period of time; a position that is, as I just found out, supported by Penrose in that same chapter, contrary to popular learned opinion.
As for Poincare recurrence theorem, I have read that the time period is too long to be considered an adequate solution to the problem. Personally, I don't really see how it solves the problem at all; if the system is going to act reversibly over millions of years, there is still a statistical anomaly between the close past and future, isn't it?
I don't understand fluctuation dissipation theorems at all so can't comment on that; can only hope that you'll explain further. Thanks.