RESUMEN
The main objective of this work [previously appeared in literature, the thermodynamical field theory (TFT)] is to determine the nonlinear closure equations (i.e., the flux-force relations) valid for thermodynamic systems out of Onsager's region. The TFT rests upon the concept of equivalence between thermodynamic systems. More precisely, the equivalent character of two alternative descriptions of a thermodynamic system is ensured if, and only if, the two sets of thermodynamic forces are linked with each other by the so-called thermodynamic coordinate transformations (TCT). In this work, we describe the Lie group and the group representations associated to the TCT. The TCT guarantee the validity of the so-called thermodynamic covariance principle (TCP): The nonlinear closure equations, i.e., the flux-force relations, everywhere and in particular outside the Onsager region, must be covariant under TCT. In other terms, the fundamental laws of thermodynamics should be manifestly covariant under transformations between the admissible thermodynamic forces, i.e., under TCT. The TCP ensures the validity of the fundamental theorems for systems far from equilibrium. The symmetry properties of a physical system are intimately related to the conservation laws characterizing that system. Noether's theorem gives a precise description of this relation. We derive the conserved (thermodynamic) currents and, as an example of calculation, a system out of equilibrium (tokamak plasmas) where the validity of TCP imposed at the level of the kinetic equations is also analyzed.
RESUMEN
In a recent paper, Phys. Rev. E 81, 041137 (2010), the author attempts to derive ten necessary conditions for the stability of dissipative fluids and plasmas. Assuming the validity of the local equilibrium principle, these criteria have been obtained solely from the first and second laws of thermodynamics. The Onsager reciprocity relations have not been invoked, and the author's results are supposed to be valid independent of the choice of the boundary conditions. In the present Comment, in agreement with the general theory established by Glansdorff-Prigogine in 1954 and 1970, we show that there is no variational principle expressing the necessary conditions for the stability of dissipative systems involving convective effects when the system is out of the Onsager region. In particular, we prove that the basic equations constituting the starting point of the analysis of the author, attempting to derive ten necessary conditions for the stability involving magnetohydrodynamical effects, are incorrect and in contradiction with the laws of the thermodynamics of irreversible processes.
RESUMEN
We present a general formula for the topology and H-flux of the T-dual of a type II compactification. Our results apply to T-dualities with respect to any free circle action. In particular, we find that the manifolds on each side of the duality are circle bundles whose curvatures are given by the integral of the dual H-flux over the dual circle. As a corollary we conjecture an obstruction to multiple T-dualities, generalizing the obstruction known to exist on the twisted torus. Examples include SU(2) Wess-Zumino-Witten models, lens spaces, and the supersymmetric string theory on the nonspin AdS5 x CP2 x S1 compactification.