  A decade ago, a macroscopic theory for closure relations has been proposed
for systems out of Onsager's region. This theory is referred to as the
"Thermodynamic Field Theory" (TFT). The aim of the work was to determine the
nonlinear flux-force relations that respect the thermodynamic theorems for
systems far from equilibrium. We propose a new formulation of the TFT where one
of the basic restrictions, namely the closed-form solution for the
skew-symmetric piece of the transport coefficients, has been removed. In
addition, the general covariance principle is replaced by the De
Donder-Prigogine thermodynamic covariance principle (TCP). The introduction of
TCP requires the application of an appropriate mathematical formalism, which is
referred to as the "entropy-covariant formalism". By geometrical arguments, we
prove the validity of the Glansdorff-Prigogine Universal Criterion of
Evolution. A new set of closure equations determining the nonlinear corrections
to the linear ("Onsager") transport coefficients is also derived. The geometry
of the thermodynamic space is non-Riemannian. However, it tends to be
Riemannian for high values of the entropy production. In this limit, we recover
the transport equations found by the old theory. Applications of our approach
to transport in magnetically confined plasmas, materials submitted to
temperature and electric potential gradients or to unimolecular triangular
chemical reactions can be found at references cited herein. Transport processes
in tokamak plasmas are of particular interest. In this case, even in absence of
turbulence, the state of the plasma remains close to (but, it is not in) a
state of local equilibrium. This prevents the transport relations from being
linear.
