Undergrad Particular configuration of a system and grand partition fn.

[Pushoam]

I don't understand how could be a particular configuration described by eqn. (29.4).
Why is it said a particular configuration?

I know that this is the grand Boltzmann factor for one particle in energy state $E_1$. But how does it describe configuration of the system?

 

[Metmann]

Why is it said a particular configuration?

I guess it is particular, because in (29.24) the numbers $n_i$ are fixed to specific values and because several combinations of occupation numbers are possible, the case of fixed occupation numbers denotes only one specific configuration. Then in (29.25) you sum over all particular configurations by taking into account all possible combinations of occupation numbers.

But how does it describe configuration of the system?

Well, (29.24) encodes the information on how many particles occupy each energy state and this is exactly what is known as the configuration.

 

[Pushoam]

Well, (29.24) encodes the information on how many particles occupy each energy state and this is exactly what is known as the configuration.

What I got is : the eq (29.4) divided by eq. (29.5) gives the probability that the system will be in such a macrostate ( thus the particular configuration) such that $n_1$ particles will be in the $E_1$ state and so on. Here the macrostate is described by {($n_1, E_1) ,(n_2,E_2), ...$}.

Right?

Thank you.

 

[Metmann]

What I got is : the eq (29.4) divided by eq. (29.5) gives the probability that the system will be in such a macrostate ( thus the particular configuration) such that n1n_1 particles will be in the E1E_1 state and so on. Here the macrostate is described by {(n1,E1),(n2,E2),...n_1, E_1) ,(n_2,E_2), ...}

No, not exactly. $\{(n_i,E_i )\}_i$ denotes a particular microstate, while the macrostate is given by temperature $T \sim \frac{1}{\beta}$ and chemical potential $\mu$. So (29.4) devided by (29.5) gives you the probability that a particular microstate is realized given the macrostate.