In the grand canonical ensemble, the control variables
are the chemical potential 
, the volume V and
the temperature T. The total particle number
N is therefore allowed to fluctuate.
It is therefore related to the
canonical ensemble by a Legendre transformation with
respect to the particle number N. Its utility lies in
the fact that it closely represents the conditions
under which experiments are often performed and,
as we shall see, it gives direct access to the
equation of state.