A question concerning derivation of canonical ensemble's probability

[zasdzcc]

In derivation of probability of system at energy E with canonical ensemble, one assumes that the probability of system in a microstate Ei is proportional to the multiplicity of reservoir. Is this probability the conditional probability by knowing that system is at energy Ei with knowing it is at state Ei? All I see is that probability of finding system in energy E is proportional to product of probabilities of system and reservoir. And for a given energy Ei for a micro state, it is possible that the system can rearrange it into a state which has the same energy but it is another microstate.

Thanks.

 

[NateD]

No, the probability of finding the system at energy Ei is not a conditional probability. It is the probability of finding the system in that microstate given that it has total energy E. The probability of finding the system in a particular microstate is proportional to the multiplicity of the reservoir, which is the number of ways the reservoir can be arranged so that the total energy of the system and the reservoir is E. There is no need to consider the rearrangement of the system into another microstate with the same energy.