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In a previous work we provided the explicit form of the nonlinear PDEs, subjected to the appropriate boundary conditions, which have to be satisfied by transport coefficients for systems out of Onsager's 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 also transport in thermodynamic systems in turbulent regime. As a special case, we derive the nonlinear PDEs for transport coefficients when the thermodynamic system is subjected to two thermodynamic forces. In this case, the obtained PDE is, in thermodynamical field theory (TFT), analogous to Liouville's equation in Riemannian (or pseudo-Riemannian) geometry. The validity of our model is tested by analysing a concrete example where Onsager's relations manifestly disagree with experience: transport in Tokamak-plasmas. More specifically, we compute the electron mass and energy losses in turbulent FTU (Frascati Tokamak Upgrade)-plasmas. We show the agreement between the theoretical predictions and experimental observations. This approach allows to predict the values of the Bohm and the gyro-Bohm coefficients. To the best of our knowledge, it is the first time that such coefficients have been evaluated analytically. The aim of this series of works is to apply our approach to the Divertor Tokamak Test facility (DTT), to be built in Italy, and to ITER. [ABSTRACT FROM AUTHOR]