  The objective of this work is to determine the nonlinear flux-force relations
for systems out of Onsager's region that respect the existing thermodynamic
theorems for systems far from equilibrium. To this aim, a thermodynamic theory
for irreversible processes [referred to as the Thermodynamical Field Theory
(TFT)] has been developed. The TFT rests upon the concept of equivalence
between thermodynamic systems: "The equivalent character of two alternative
descriptions of a thermodynamic system is ensured if, and only if, the entropy
production and the Glansdorff-Prigogine dissipative quantity remain unaltered
under the thermodynamic forces transformation". The TCT leads naturally to the
"Thermodynamic Covariance Principle" (TCP) stating that "The nonlinear closure
equations, i.e., the flux-force relations, must be covariant under TCT". In
this work, we provide the explicit expression of the nonlinear PDEs, subjected
to the appropriate boundary conditions, which have to be satisfied by transport
coefficients when the skew-symmetric piece is absent. The solution of these
equations allows to determine the flux-force closure relations for systems out
of the Onsager region. Since the proposed PDEs are obtained without neglecting
any term present in the balance equations (i.e., the mass, momentum, and energy
balance equations), we propose them as a good candidate for describing
transport in thermodynamic systems also in turbulent regime. A preliminary test
is carried out by analysing a concrete example where Onsager's relations
manifestly disagree with experience: losses in magnetically confined
Tokamak-plasmas in fully collisional and in turbulent regimes. We show the good
agreement between the theoretical predictions and the experimental data. The
aim is to apply our approach to the "Divertor Tokamak Test facility" (DTT), to
be built in Italy, and to ITER.
