# Entropy correction term?

1. Apr 26, 2009

### Gerenuk

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

For one particle in each state for example
$$S=-s\ln n+\frac12 s\ln n$$

(oh weird; my browser doesn't show the equations. I hope they are displayed correctly)

Last edited: Apr 26, 2009