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Statistical Mechanics Derivation

  1. Jan 20, 2010 #1
    1. The problem statement, all variables and given/known data

    From Landau and Lifgarbagez:

    [tex]\langle (\Delta f)^{2} \rangle = \overline{f^{2}} - (\overline{f})^{2}[/tex]

    This isn't derived, just stated, and I'd like to understand how it comes about. f is a generic quantity "relating to a macroscopic body or to a part of it."

    2. Relevant equations

    [tex]\Delta f = f - \overline{f}[/tex]

    3. The attempt at a solution

    [tex](\Delta f)^{2} = (f-\overline{f})^{2} = f^{2} - 2f \overline{f} + \overline{f}^{2}[/tex]

    Basically, I don't know how to do the averaging (not without explicit values of f, anyhow).
  2. jcsd
  3. Jan 20, 2010 #2


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    You put angle brackets around it or put a bar over it. ;)

    Remember that [tex]\overline{f}[/tex] is a constant, and use the fact that

    [tex]\langle \alpha f+\beta g\rangle = \alpha\langle f\rangle+\beta\langle g\rangle[/tex]

    where [itex]\alpha[/itex] and [itex]\beta[/itex] are constants.
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