Properties of Conservation-dissipation Formalism of Irreversible Thermodynamics

TL;DR

This paper introduces a formalism for modeling irreversible thermodynamic processes using PDEs, establishing fundamental requirements, and demonstrating how the conservation-dissipation formalism (CDF) satisfies these, with improvements via Maxwell iteration.

Contribution

It presents a new formalism (CDF) for deriving PDEs in irreversible thermodynamics, including constraints, enhancements, and a refined second law characterization.

Findings

CDF-derived PDEs meet fundamental thermodynamic requirements

Maxwell iteration preserves gradient structure and dissipativeness

Refined second law characterizes strong dissipativeness

Abstract

This paper proposes four fundamental requirements for establishing PDEs (partial differential equations) modeling irreversible processes. We show that the PDEs derived via the CDF (conservation-dissipation formalism) meet all the requirements. In doing so, we find useful constraints on the freedoms of CDF and point out that a shortcoming of the formalism can be remedied with the help of the Maxwell iteration. It is proved that the iteration preserves the gradient structure and strong dissipativeness of the CDF-based PDEs. A refined formulation of the second law of thermodynamics is given to characterize the strong dissipativeness, while the gradient structure corresponds to nonlinear Onsager relations. Further advantages and limitations of CDF will also be presented.