Thermodynamic Field Theory with the Iso-Entropic Formalism

TL;DR

This paper introduces a revised thermodynamic field theory using the iso-entropic formalism, removing previous restrictions, and providing new nonlinear transport equations applicable to complex systems like plasmas and chemical reactions.

Contribution

It presents a new formulation of TFT with the iso-entropic formalism, replacing the closed-form solution restriction and incorporating Prigogine's TCP for nonlinear transport analysis.

Findings

Proves the universal criterion of evolution using geometrical methods.

Derives new nonlinear thermodynamic field equations.

Shows the geometry tends to Riemannian at high entropy production.

Abstract

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.