Statistical derivation of the NVT partition function

Taking the natural logarithm of both sides yields In Q(N, V, T) = In V, ( ))exp 

The equivalence of ensembles becomes apparent at the thermodynamic limit. Regardless of the ensemble constraints, a system at equilibrium will attain one observable value for each thermodynamic state variable. 

It is instructive before discussing other ensembles to present a different statistical derivation of the iVET partition function. 

Consider an ensemble of NVT systems (Fig. 6.2). Assume the size of the systems to be large enough to satisfy the thermodynamic hmit requirement. Assume also that this ensemble is isolated from the rest of the universe and has an overall constant energy S. If all the systems in the ensemble are in thermal contact with each other, their temperatures will be the same at equilibrium, that is Ti = T2 = = Tj.  

In principle, the energy of each of the systems can fluctuate, assuming any one of J energy levels, Ei, E2, Ej, where J is arbitrarily large (/ 00). 

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Statistical derivation of the NVT partition function where the sum runs over all microscopic states, or... 

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