# Partition function in Statistical Physics

1. Sep 20, 2010

### Hymne

Hi! I am for the moment reading a course in statistical physics where the author has definied not less then three diffrent partitionfunctions.

W, Z an Z which are called the microcanonical partitionfunction, canonical partitionfunction (?) and the grand canonical partitionfunction.

I have how ever a hard time keeping track of under which conditions to use which and what we assume that the system satifies when we use one of them.

2. Sep 20, 2010

### nonequilibrium

microcanonical <-> E,V,N <-> isolated system (e.g. the universe (?), a very good coolbox)
canonical <-> T,V,N <-> closed rigid system that can exchange energy (e.g. a bottle in the coolbox)
grand canonincal <-> T,V,µ <-> open rigid system = exchange of energy and particles (e.g. the upper half of the bottle)

$$1/T := \frac{\partial S}{\partial <E>}$$ and $$-\mu / T := \frac{\partial S}{\partial <N>}$$

By their definitions you can see that they indeed characterize respective equilibrium in case of equality for both systems in contact.