Talk:Partition function (statistical mechanics)
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Shouldn't the first title read 'Classical', instead of 'Classic'? Unless, of course, 'Classic' means something specific in this context. Gokul
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[edit] For the canonical ensemble partition function: Q versus Z
For the canonical ensemble, should Q be used in place of Z? Z is actually a special case (the momentum component is factored out) often called the configuration integral. Ref "Understanding Molecular Simulation" 2nd Ed. Frenkel and Smit
- No. There is no standard notation, so this change is not necessary. -- CYD
i think d/dbeta of minus average energy gives the average squared energy.
so the second derivative wrt beta of ln Z gives the second moment of energy, not the second central moment as indicated
[edit] A good book
I suggest a good book to read. Fedrick Beif's Statistical and Thermal Physics. Of course-by the way can someone discuss your comment about it between other authors' books.--GyBlop 10:50, 28 February 2006 (UTC)
I think that's Frederick Reif (or at least that's how it's spelled in my edition). Flutefreek 05:44, 2 November 2006 (UTC)
[edit] Sum and Integral
Hello..something is fuzzy in the article for example if we have a certain system with a Hamiltonian H and energies En my question is..what partition function should we use?..
-The expression given by the Sum 
-Or the expression given by the Integral 
But clearly Z1 and Z2 are different, the problem is how can you calculate the Partition function if you don,t know the energies of the system (Hamiltonian too much difficult to solve) and if approximately Z1˜Z2
- En is energy of a certain state (indexed by n under assumption that number of states is countable). In the case of the integral, the state of the system is determined by p and q, and there is a continuum of possible states. In both cases the meaning of the partition function stays the same. There is however a disagreement in using the degeneracy factor, it is used in the definition but nowhere else, I think I ll try to rephrase the article now.(Igny 17:23, 18 July 2006 (UTC))
- Those two are used in different contexts, shouldn't be confused. Z1 is the quantum mechanical partition function. The summation is over number of distinct energy eigenvalues. It is, assuming some technical conditions hold, the trace of exp(-β H), where H is the quantum mechanical Hamiltonian. If you sum over energy eigenvalues including multiplicity, then the degeneracy g(n) would be removed from the expression. On the other hand, Z2 describes the classical canonical ensemble, therefore is a normalization factor for a probability measure on the phase space. Mct mht 21:32, 18 July 2006 (UTC)
[edit] Error in article
BTW, there is an error in the article. The so called "coarse graining" refers to semiclassical treatment of quantum mechanical ensembles, not classical systems. For classical systems, the factor 1/h3N shouldn't be there. Mct mht 02:33, 19 July 2006 (UTC)
[edit] Calculating the thermodynamic total energy
In the Calculating the thermodynamic total energy section shouldn't it say "and then set λ to one," rather than "and then set λ to zero"? If I follow the argument correctly, it is essentially an application of perturbation theory, in which you expand the change in the Hamiltonian (A in this case) in small λ and then set λ to one at the end, not to zero, because this would cancel out the perturbative terms. --zipz0p 20:05, 11 October 2006 (UTC)
