The inverse Burnett coefficients are defined in terms of the
derivatives with respect to the flux of the average of a
thermodynamic force in an ensemble where the flux is fixed
value. In this section, we demonstrate the equivalence of this
and derivatives with respect to the flux in a canonical
ensemble. The subset of the canonical ensemble in which the
flux takes on a specific value of J is called the 
-ensemble. One may write a phase average <B> as an
integration over all possible 
-ensembles
where 
is the probability that the flux takes on a
specific value J, and 
is the phase average in the
-ensemble.
In the thermodynamic limit, 
will be clustered about 
with infinitesimal spread, suggesting that we can write a Taylor
series expansion of 
about 
:
Substituting this into (
), we find that
From Appendix , 
is
of order 
in the large system limit, and so it is clear that the
ensemble corrections are of order 
.
