The Thermodynamic Covariance Principle

TL;DR

This paper revises the concept of thermodynamic equivalence between systems, introducing Thermodynamic Coordinate Transformations (TCT) that preserve key thermodynamic quantities and relations, leading to the Thermodynamic Covariance Principle (TCP).

Contribution

It defines the class of transformations (TCT) that preserve entropy production and dissipative quantities, extending the covariance principle beyond linear regimes.

Findings

TCT preserve reciprocity relations even outside the Onsager region.

The Thermodynamic Covariance Principle applies to nonlinear thermodynamic equations.

A general class of transformations satisfying TCT is determined.

Abstract

The concept of {\it equivalent systems} from the thermodynamic point of view, originally introduced by Th. De Donder and I. Prigogine, is deeply investigated and revised. From our point of view, two systems are thermodynamically equivalent if, under transformation of the thermodynamic forces, both the entropy production and the Glansdorff-Prigogine dissipative quantity remain unaltered. This kind of transformations may be referred to as the {\it Thermodynamic Coordinate Transformations} (TCT). The general class of transformations satisfying the TCT is determined. We shall see that, also in the nonlinear region ({\it i.e.}, out of the Onsager region), the TCT preserve the reciprocity relations of the transformed transport matrix. The equivalent character of two transformations under TCT, leads to the concept of {\it Thermodynamic Covariance Principle} (TCP) stating that all thermodynamic equations involving the thermodynamic forces and flows ({\it e.g.}, the closure flux-force relations) should be covariant under TCT.