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The grand potential and total Helmholtz free energy

  1. Feb 1, 2015 #1
    what's the relation of the grand potential [itex]J=F-\mu N[/itex] and total Helmholtz free energy of "system and particle environment" [itex]F^{tot}[/itex]?
    In K. Sekimoto's book "Stochastic Energetics" P182, P310 and P311 (see screenshots in the link):
    Does it mean the followings:[itex]J=lim[F_{tot}-\mu N_{tot}], lim[F^c]=lim[\mu(N_{tot}-N)], lim[\Omega^cf^c]=lim[\mu N_{tot}][/itex],
    And the right term of the formula above A.77 seems to be lack of a factor [itex]\frac{N_{tot}^{N_{tot}}}{N_{tot}!}[/itex],which is infinite when [itex]N_{tot}->\infty[/itex].
    Last edited: Feb 1, 2015
  2. jcsd
  3. Feb 2, 2015 #2
    Google book of Stochastic Energetics: link
    Is there any problem in the formula A.75(p310) and the first formula in p311?
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