A deeper look at the thermodynamic field equations

Abstract

The Thermodynamic Field Theory (TFT) allows to deal with thermodynamic systems submitted even to strong non-equilibrium conditions. This theory, formulated in previous works, enables to find field equations whose solutions give the generalised relations between the thermodynamic forces and their conjugate flows. It has been shown that the evolution of the thermodynamic systems is well described in Weyl's space. In the particular case in which the thermodynamic forces and conjugate flows are linked only through a symmetric tensor (the metric tensor), the resulting geometry is the Riemannian geometry. When Weyl's space is even-dimensional, the thermodynamic space introduced in refs. [1-4] results to be a differentiable symplectic manifold. In this paper, I shall point out the subtlety in the derivation of the thermodynamic field equations. We shall see that this analysis will allow to better understand the physical hypotheses which are at the basis of the TFT. Successively, we shall treat spatially extended thermodynamic systems and we shall find equations able to determine stationary solutions and critical points for systems away from equilibrium and submitted to time-independent boundary conditions. At the end of the paper, we shall introduce the symplectic thermodynamic spaces.