Variational multi-fluid dynamics and causal heat conductivity

TL;DR

This paper presents a variational multi-fluid model treating entropy as a dynamical entity to derive causal heat conduction, linking entropy entrainment to thermal relaxation time and relating non-local effects to phonon hydrodynamics.

Contribution

It introduces a novel variational multi-fluid framework for heat conduction that reproduces extended irreversible thermodynamics results and incorporates causality and non-local effects.

Findings

Entropy entrainment relates to thermal relaxation time.

The model reproduces key results of extended irreversible thermodynamics.

Non-local terms naturally emerge and connect to phonon hydrodynamics.

Abstract

We discuss heat conductivity from the point of view of a variational multi-fluid model, treating entropy as a dynamical entity. We demonstrate that a two-fluid model with a massive fluid component and a massless entropy can reproduce a number of key results from extended irreversible thermodynamics. In particular, we show that the entropy entrainment is intimately linked to the thermal relaxation time that is required to make heat propagation in solids causal. We also discuss non-local terms that arise naturally in a dissipative multi-fluid model, and relate these terms to those of phonon hydrodynamics. Finally, we formulate a complete heat conducting two-component model and discuss briefly the new dissipative terms that arise.