- #36
atyy
Science Advisor
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Zacku said:So I agree with your comment atyy, there must be something else than only statistical inference (except for the microcanonical case i would say) to explain canonical ensembles. Noting that it doesn't solve the problem of the existence, or not, of a real ensemble distrubution probability for system at equilibrium.
Yes, I agree we do not have a good mathematical understanding from microscopic dynamics why the equilibrium ensembles work so well (even the microcanonical case). I guess quite a bit of computational work has been done showing that almost any microscopic dynamics reproduce the equilibrium ensembles. But that's different from having a theorem.
Actually, I was told by someone working on dynamical systems quite a few years back, that computational work suggested that the KAM theorem would "hold" beyond the limits of the mathematical proof - just as experience and computation suggest that we should have more than the ergodic theorem for statistical mechanics.