Talk:Microstate (statistical mechanics)

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Why is there a finite number of microstates?? Quantum physics wasn't around when the idea was invented....help please.

There isn't classically, (since even infinitesimally close states in phase space are possible) - that's why you show that it's reasonable to assume that they're uniformly distributed through a given volume of phase space.

[edit] Entropy

I always think of entropy of the i-th macrostate as S_i=\ln(W_i)\, where W_i\, is the number of microstates in the i-th macrostate. Can you remind me how this relates to the use of the pi which from your definition is p_i=W_i/\sum_i W_i\,? Thanks PAR 05:57, 4 November 2005 (UTC)

In fact I'm not sure exactly what you mean by "i-th macrostate." But I think I understand the question though. The expression I gqve in the article works for just any system, including far away from thermodynamic equilibrium (have yet to mention that, but it's in order).
Then an isolated system keeps the same energy, so that it fluctuates between those of his microstates that have a given energy. Such microstates number \Omega(E)~. In this framework the general expression of S given in the article is maximal when all states are equally likely:
p_1 = \ldots = p_N = \frac{1}{\Omega (E)}
And in this framework the expression of the entropy from the article reduces to:
S = -k_B log (\Omega (E))~, which is Boltzman's definition of entropy. In fact it is only valid at thermodynamic equilibrium, for an isolated system. For a non-isolated system, even at thermodynamic equilibrium, it's not Boltzman's entropy that works.ThorinMuglindir 13:06, 4 November 2005 (UTC)
oh my god... I understand why your question was somehow unclear to me: I did a mistake yesterday in defining Ei and pi. In reality p_i is the proba associated with microstate i (and not macro as I first wrote), and Ei is the energy level of this microstate, which is also an energy level of the system. Thanks for helping me realize this. will correct at once.ThorinMuglindir 13:17, 4 November 2005 (UTC)
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