Weakly nonlocal nonequilibrium thermodynamics: the Cahn-Hilliard equation

TL;DR

This paper derives the Cahn-Hilliard and Ginzburg-Landau equations from thermodynamic principles using a rigorous Liu procedure, providing a non-variational foundation for these models.

Contribution

It introduces a thermodynamic derivation of phase-field equations using Liu's method, avoiding traditional variational approaches.

Findings

Derivation of Cahn-Hilliard and Ginzburg-Landau equations from second law

Support for divergence separation approach with rigorous thermodynamics

Clarification of the role of functional derivatives in thermodynamic context

Abstract

The Cahn-Hilliard and Ginzburg-Landau (Allen-Cahn) equations are derived from the second law. The intuitive approach by separation of full divergences is supported by a more rigorous method, based on Liu procedure and a constitutive entropy flux. Thermodynamic considerations eliminate the necessity of variational techniques and explain the role of functional derivatives.