restfull Posted February 14, 2006 Share Posted February 14, 2006 I was wondering if anyone could explain the underlying significance of the form of Boltzmann's formulation of Entropy S = k ln (omega) where omega is the number of microstates. Why is it that the entropy increases with the log of omega? Link to comment Share on other sites More sharing options...
timo Posted February 15, 2006 Share Posted February 15, 2006 Well, it´s simply a definition; although it´s suited to get in contact with the entropy defined in (nonstatistical-) thermodynamics. Some properties which make it look like a good choice to me: 1) As long as the map from the number of microstates to entropy is a monotonous rising one (A > B => log(A) > log(B) ), the very important "the system will be in the macrostate with the most associated microstates"-axiom still translates to "entropy will be at maximum". 2) It seems like a practical definition: I can imagine you often encounter problems where you multiply numbers of microstates. Since log(A*B) = log(A)+log(B), entropy is an additive number for those problems. Sry for being so vague in point 2 but I don´t have a good example in mind right now; perhaps someone else has. Either way: From the physics-side, it doesn´t really matter if you take the log or not; it changes the equations but it´s still the same physical entity. Perhaps it´s comparable to measuring temperature in Fahrenheit or Kelvin, only a tick more sophisticated. Link to comment Share on other sites More sharing options...
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