Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Boltzmann factor and partition function
  1. Partition functions (Replies: 3)

  2. Partition function (Replies: 2)