  We provide a concrete formula for a dual system as well as for a conjugate
system of $q$-Gaussians represented on the $q$-deformed Fock space. Moreover,
using this formula, we prove the existence of a free Gibbs potential and that
the non-microstates free Fisher information is finite for any $q$ with
$-1<q<1$, which is an improvement on a previous result of Y. Dabrowski. We also
indicate how our results can be extended to the more general setting of mixed
$q_{ij}$-relations.
