# Entropy production in phase field theories

## TL;DR

This paper develops a thermodynamic framework to analyze entropy production in phase field theories, specifically for Allen-Cahn dynamics with heat conduction, using non-equilibrium thermodynamics methods.

## Contribution

It introduces a novel thermodynamic approach to quantify entropy production in phase field models with heat conduction, extending classical methods.

## Key findings

- Entropy production is explicitly calculated for Allen-Cahn dynamics.
- The framework accounts for heat conduction in phase field models.
- Classical irreversible thermodynamics methods are applied to nonlocal internal variables.

## Abstract

Allen-Cahn (Ginzburg-Landau) dynamics for scalar fields with heat conduction is treated in rigid bodies using a non-equilibrium thermodynamic framework with weakly nonlocal internal variables. The entropy production and entropy flux is calculated with the classical method of irreversible thermodynamics by separating full divergences.