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Standard deviation of the energy of a system in a heat bath

  1. Aug 29, 2008 #1
    Given the mean energy of a system in a heat bath is

    \bar{E} = - \frac{\partial ln(Z)}{\partial \beta}

    Where Z is the partition function and [tex]\beta = k_BT[/tex]

    Why is the standard deviation of E defined by:

    (\Delta E)^2 = \frac{\partial^2 ln(Z)}{\partial \beta ^2}

    I can't seem to find any proof of how the second derivative is related to the standard deviation.
  2. jcsd
  3. Aug 29, 2008 #2


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  4. Aug 29, 2008 #3
    Thanks a lot those notes are also pretty useful in other respects as well.
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