  Finite thermostats are studied in the context of nonequilibrium statistical
mechanics. Entropy production rate has been identified with the mechanical
quantity expressed by the phase space contraction rate and the currents have
been linked to its derivatives with respect to the parameters measuring the
forcing intensities. In some instances Green-Kubo formulae, hence Onsager
reciprocity, have been related to the fluctuation theorem. However, mainly when
dissipation takes place at the boundary (as in gases or liquids in contact with
thermostats), phase space contraction may be independent on some of the forcing
parameters or, even in absence of forcing, phase space contraction may not
vanish: then the relation with the fluctuation theorem does not seem to apply.
On the other hand phase space contraction can be altered by changing the metric
on phase space: here this ambiguity is discussed and employed to show that the
relation between the fluctuation theorem and Green-Kubo formulae can be
extended and is, by far, more general.
