Quite a long title :D The fundamental assumption of statistical mechanics states, that all microstates of a system are equally probable. From what I know Liouvilles theorem should support this, but other than that I think it is just a pure assumption. Now I'm not really sure if I find it intuitive. Suppose you have one system with 100 quantum oscillators storing each one energy unit and it's put in contact with another solid storing no energy but which also consists of 100 quantum oscillators. Then the fundamental assumption says that, the energy will get passed around randomly such that all the combined microstates are equally probable. But why doesn't it consider the case where the quantum oscillators in solid one exchange energy with each other? I mean for instance, why can't oscillator one with one unit of energy not transfer energy to oscillator two which also transfers energy back to oscillator one such that not overall change has happened - i.e. solid one still has 100 oscillators with one energy unit in each? (Or maybe that wouldnt matter when I think about it because then for the others there would also be 100! ways of arranging them..)
There's some work trying to justify the assumptions of statistical mechanics from the dynamics of a pure quantum state. http://arxiv.org/abs/1108.0928 http://arxiv.org/abs/cond-mat/0511091 http://arxiv.org/abs/quant-ph/0511225