Entropy

Thread Starter

boks

Joined Oct 10, 2008
218
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?
 

rspuzio

Joined Jan 19, 2009
77
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.

\( S = -k \sum_i P_i \ln P_i\)
 
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