Entropy

Discussion in 'Physics' started by boks, Aug 24, 2009.

  1. boks

    Thread Starter Active Member

    Oct 10, 2008
    218
    0
    I have seen two different entropy equations:

    1. S = -k /Sigma_i P_i ln P_i

    and

    2. S = k lnW, where W is the multiplicity.

    I'm trying to calculate the entropy for an experiment where I sample the sock colors of 30 students and find the distribution of the colors of the socks they are wearing. I'm a little surprised to find that the two equations give me different entropy values. Why is that?
     
  2. rspuzio

    Active Member

    Jan 19, 2009
    77
    0
    The former equation is the more general one; the latter
    is what it reduces to when all the P_i's are
    equal (uniform probability distribution). However, as
    you wrote them, there is a typo --- there should be no
    division sign in the first equation, i.e.

     S = -k \sum_i P_i \ln P_i
     
    Last edited: Aug 24, 2009
  3. boks

    Thread Starter Active Member

    Oct 10, 2008
    218
    0
    thanks a lot
     
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