In this appendix, we show that the phase average of a product of intensive
phase variables 
is of order 
, with N being
the number of particles in the system.
Let us begin by noting that the phase variable 
can be written as an
average over individual particles:
Then we find that
In a system where the order is short range (for example a fluid far from its
critical point), we would expect that correlations of the form
only picks up contributions from its nearest neighbours, and is
consequently intensive. More generally, we can say that 
is intensive. The first term on the right hand side of
(
) is clearly intensive, so we find
