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Entropy correction term?

  1. Apr 26, 2009 #1
    I assumed that entropy derives from combinatorics so I calculated
    [tex]S=\ln \frac{\prod_{i=1}^S n_k!}{n!}[/tex]
    for n particles in S states. The result is
    [tex]S=\ln \frac{\prod_{i=1}^S n_k!}{n!}=n\sum_{i=1}^S p_i\ln p_i+\frac12 s\ln n[/tex]
    if [itex]p_i=n_i/n[/itex] and [itex]\ln n/n\ll S[/itex]
    What about the second correction term? Can it not play a role?

    For one particle in each state for example
    [tex]S=-s\ln n+\frac12 s\ln n[/tex]

    (oh weird; my browser doesn't show the equations. I hope they are displayed correctly)
     
    Last edited: Apr 26, 2009
  2. jcsd
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