  In this paper we suggest that in the framework of the Category Theory it is
possible to demonstrate the mathematical and logical \textit{dual equivalence}
between the category of the $q$-deformed Hopf Coalgebras and the category of
the $q$-deformed Hopf Algebras in QFT, interpreted as a thermal field theory.
Each pair algebra-coalgebra characterizes, indeed, a QFT system and its
mirroring thermal bath, respectively, so to model dissipative quantum systems
persistently in far-from-equilibrium conditions, with an evident significance
also for biological sciences. The $q$-deformed Hopf Coalgebras and the
$q$-deformed Hopf Algebras constitute two dual categories because characterized
by the same functor $T$, related with the Bogoliubov transform, and by its
contravariant application $T^{op}$, respectively. The \textit{q}-deformation
parameter, indeed, is related to the Bogoliubov angle, and it is effectively a
thermal parameter. Therefore, the different values of $q$ identify univocally,
and then label, the vacua appearing in the foliation process of the quantum
vacuum. This means that, in the framework of Universal Coalgebra, as general
theory of dynamic and computing systems ("labelled state-transition systems"),
the so labelled infinitely many quantum vacua can be interpreted as the Final
Coalgebra of an "Infinite State Black-Box Machine". All this opens the way to
the possibility of designing a new class of universal quantum computing
architectures based on this coalgebraic formulation of QFT, as its ability of
naturally generating a Fibonacci progression demonstrates.
