Meaning of formula from statistical physics

[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 :-)

 

[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 textbook but, eh, gets the job done )
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.

 

[rachmaninoff]

http://en.wikipedia.org/wiki/Entropy#Mathematical_description

If the p's are all identical, the entropy reduces to cyrus' textbook's version.

 

[broegger]

Ok, thanks guys!