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?

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    $\begingroup$ Read your second 'isn't allowed' link a little more closely. The whole point of the Grand Canonical Ensemble is that the system is allowed to interchange both particles and energy with the reservoir. $\endgroup$ Apr 15, 2011 at 22:03

1 Answer 1


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.


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