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Boltzmann factor and partition function

  1. Sep 15, 2005 #1
    I got a problem by finding an proper explanation.

    The Boltzmann factor is defined as
    [itex]P_j=\frac{1}{Z}e^{-\beta E_j}[/itex]
    I know, this is a probability distribution. but what exactly does it mean?

    Wikipedia says: "The probability Pj that the system occupies microstate j" (link)
    But that doesen make sense to me. cos [itex]\sum_i[/itex] is equal to 1.
    That would only make sense if i look at ONLY 1 particle and not a system with n particles IMHO.

    Then i got this Partition function Z.
    It is defined as [itex]Z=\sum_i g_i e^{- \frac{E_i}{k_BT}[/itex]
    with a factor gi denoting the degeneracy of energy states.

    What is gi? i thought it's the number of different states in this energy level. but that's not likely cos in the Maxwell-Boltzmann distribution there's no pauli law...


  2. jcsd
  3. Sep 15, 2005 #2


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    If it didn't add up to 1, then it wouldn't be a probability now, would it? :tongue:

    Anyways, the quote talks about the microstates of the system: in other words, it would include something about the state of each individual component of the system.
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