# Microcanonical vs canonical vs grand canonical ensemble

gizzmo
Can somebody explain to me the differences between the ensembles, and how does this differences refer to experiment?

I know that:

Microcanonical ensemble is a concept used to describe the thermodynamic properties of an isolated system. Possible states of the system have the same energy and the probability for the system to be in any given state is the same. So, it describes a system with a fixed number of particles ("N"), a fixed volume ("V"), and a fixed energy ("E").

Canonical ensemble describes a system where the number of particles ("N") and the volume ("V") is constant, and it has a well defined temperature ("T"), which specifies fluctuation of energy.

Grand canonical ensemble describes a system with fixed volume ("V") and temperature ("T") but to specify the fluctuation of the number of particles it introduces chemical potential ("mu").

But, how does that relate to experiment? Can you give me real life examples for those ensembles.

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paweld
In practice all thermodynamic quantities like internal energy, entropy,
preassure, etc. derived from these ensembles should be equal.
There will be only differences in fluctuations of these parameters.
If you want to theoretically predict the magnitude of fluctuation
of let's say energy of a gas which is kept in closed container at
constatnt temperature you have to use canonical ensemble
(in microcanonical ensemble the fluctuation of energy is 0).
If you want to determine the fluctuation of number of particles
the grand canonical enesemble would be a good choice, etc.