** Previous:** 5.1 The Gibbs Distribution

##

The grand potential

The grand potential is

So
. Note that two of the variables and are intensive,
so , being extensive, must be simply proportional to , the only extensive one:
.
But

This also follows from the fact that is just the Gibbs free energy per particle (see here),
so
and hence
.

The fact that is so
simple doesn't lessen its formal utility in statistical mechanics.

** Previous:** 5.1 The Gibbs Distribution
Judith McGovern
2004-03-17