Need help in statistical mechanics' canonical ensemble

[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.

 

[LightHero]

No, the probability of finding the system in energy Ei is not conditional probability. It is simply the probability of the system being in the microstate Ei, given the energy E. The multiplicity of the reservoir is a measure of how many different states of the system can have the same energy Ei, and it is that measure which is used to calculate the probability of the system being in energy Ei. In other words, the probability of the system being in energy Ei is directly proportional to the multiplicity of the reservoir.