# Meaning of formula from statistical physics

1. Mar 19, 2006

### broegger

Hi.

Can anyone explain the meaning of this formula from statistical physics to me:

$$S = -k\sum_r{p_r\ln p_r}$$​

Ok, I know that S is the entropy, the p's are probabilities of some sort - but somehow this is not satisfactory :-)

2. Mar 20, 2006

### Cyrus

What this formula tells you is that for each state of macroscopic equilibrium there corresponds a large number of possible microscopic states or molecular configurations. The entropy, s, of a system is related to the total number of possible microscopic states of that system, called the thermodynamic probability p, by the Boltzmann relation:

$$S= k*ln(p)$$

So from a microscopic point of view, the entropy of a system increases when the molecular randomness or uncertainty increases.

(stole most of that from my text book but, eh, gets the job done :tongue:)
Edit: Your formula is slightly different from mine. It appears that yours takes on the form of a probability mass function, where the sum over all r should equal to one.

Last edited: Mar 20, 2006
3. Mar 20, 2006

### rachmaninoff

4. Mar 20, 2006

### broegger

Ok, thanks guys!