Statistical Mechanics: Using 3 Ensembles for Problem Solving

[hokhani]

could we use three ensembles(microcanonic, canonic, grandcanonic) in cases of each problems?
or
can we solve any problem by using every one of these ensembles?

 

[A. Neumaier]

could we use three ensembles(microcanonic, canonic, grandcanonic) in cases of each problems?
or
can we solve any problem by using every one of these ensembles?

The grand canonical ensemble is the most useful one, as it can handle all problems.
The others are of far more limited general utility, but have occasional advantages.

For statistical mechnaics thermodynamics in terms of the grand canonical ensemble only,
see, e.g., Part II of http://lanl.arxiv.org/abs/0810.1019

 

[torquil]

could we use three ensembles(microcanonic, canonic, grandcanonic) in cases of each problems?
or
can we solve any problem by using every one of these ensembles?

Near the top of the following two pages there are mentioned limitations of the microcanonical and canonical ensemble formalisms:

http://en.wikipedia.org/wiki/Microcanonical_ensemble
http://en.wikipedia.org/wiki/Canonical_ensemble