In: Physics
I was doing some reading on wikipedia and found it interesting that one page says the Grand Canonical Ensemble does not allow for exchange of particles, however another page says it does. So I went on google books and tried to look for a more trust worthy source, again the same happens one source says it allows the other says it doesn't so which is it?
Book that says it does allow exchange: http://www.scribd.com/doc/52426748/46/Grand-Canonical-Ensemble
Another that says it isn't allowed: http://books.google.co.uk/books?id=5sd9SAoRjgQC&pg=PA62&dq=grand+canonical+ensemble+exchange+particles&hl=en&ei=hL6oTZ2THc_p4wbEh-3DCg&sa=X&oi=book_result&ct=result&resnum=1&ved=0CC0Q6AEwAA#v=onepage&q=grand%20canonical%20ensemble%20exchange%20particles&f=false
What gives?
There are, essentially, three types of ensembles used in thermodynamics:
Microcanonical Ensemble: This is used to describe closed
systems. The number of particles and the total energy are constant
(since no interaction with the environment takes place). In such a
system, the entropy will eventually be maximized.
Canonical Ensemble: Now, your system is in contact with a big
reservoir and allowed to exchange energy with the system. This
means that your system will be in thermal equilibrium with the
bath.
Grand Canonical Ensemble Now, your system can exchange both energy
and particles with the system. Hence, it will be in thermal
equilibrium with the bath and in chemical equilibrium, i.e. the
chemical potential for adding a particle to your system equals the
chemical potential for adding a particle to the bath.
If exchanging particles wasn't allowed in the grand canonical ensemble, it would become the canonical ensemble.