  A new formulation of the thermodynamic field theory (TFT) is presented. In
this new version, one of the basic restriction in the old theory, namely a
closed-form solution for the thermodynamic field strength, has been removed. In
addition, the general covariance principle is replaced by Prigogine's
thermodynamic covariance principle (TCP). The introduction of TCP required the
application of an appropriate mathematical formalism, which has been referred
to as the iso-entropic formalism. The validity of the Glansdorff-Prigogine
Universal Criterion of Evolution, via geometrical arguments, is proven. A new
set of thermodynamic field equations, able to determine the nonlinear
corrections to the linear ("Onsager") transport coefficients, is also derived.
The geometry of the thermodynamic space is non-Riemannian tending to be
Riemannian for hight values of the entropy production. In this limit, we obtain
again the same thermodynamic field equations found by the old theory.
Applications of the theory, such as 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.
