# canonical and microcanonical ensemble

What does one mean by canonical and micro canonical ensemble in statistical mechanics? Can one elaborate on this in a very simple way with examples? Pardon me, if it is a very simple thing; I am a math student.

-

Microcanonical ensemble means an isolated system with defined energy. The system may be found only in microscopic state with the adequate energy, with equal probability.

Canonical ensemble means a system attached to the "temperature reservoir", which may supply/take infinite amount of energy. The system may be found in any microscopic state, with probability proportional to the Boltzmann factor.

-
Thanks valdo for the very concise and clear answer. –  Ashok Nov 16 '11 at 5:42