Boltzmann distribution

[Moetasim]

Physical systems are analog computers and sample their states according to boltzmann distribution, this is what usually taken as granted in solving so many problems in statistical physics. what actually is the physics of boltzmann distribution....anyone....?

[Alexander]

Bol'tsman comes from statistics of similar (=indistinguashable) particles: n(E)=(exp(E/kT)+/-1)-1, plus corresponds to fermions minus - to bosons. In the classic case (kT<<E) you get n(E) ~ exp(-E/kT) which is Boltsmann distribution.

Statistics of similar particles is just a combinatorics (permutations and combinations), which in turn comes from arithmetic.