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Meaning of formula from statistical physics

  1. Mar 19, 2006 #1

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

    [tex]S = -k\sum_r{p_r\ln p_r}[/tex]​

    Ok, I know that S is the entropy, the p's are probabilities of some sort - but somehow this is not satisfactory :-)
  2. jcsd
  3. Mar 20, 2006 #2
    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:

    [tex] S= k*ln(p) [/tex]

    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
  4. Mar 20, 2006 #3
  5. Mar 20, 2006 #4
    Ok, thanks guys!
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