# The grand potential and total Helmholtz free energy

1. Feb 1, 2015

### xibeisiber

what's the relation of the grand potential $J=F-\mu N$ and total Helmholtz free energy of "system and particle environment" $F^{tot}$?
In K. Sekimoto's book "Stochastic Energetics" P182, P310 and P311 (see screenshots in the link):
Does it mean the followings:$J=lim[F_{tot}-\mu N_{tot}], lim[F^c]=lim[\mu(N_{tot}-N)], lim[\Omega^cf^c]=lim[\mu N_{tot}]$,
And the right term of the formula above A.77 seems to be lack of a factor $\frac{N_{tot}^{N_{tot}}}{N_{tot}!}$,which is infinite when $N_{tot}->\infty$.

Last edited: Feb 1, 2015
2. Feb 2, 2015

Nobody?:L:L