A consistent first-order model for relativistic heat flow

TL;DR

This paper develops a first-order relativistic heat conduction model that remains consistent with higher-order theories, ensuring stability and causality, and predicts phenomena like second sound in heat transfer.

Contribution

It demonstrates how to derive a consistent first-order model from a variational approach, addressing stability and causality issues in relativistic heat flow.

Findings

The model avoids instabilities and acausal signals.

It predicts the existence of second sound in heat.

The model aligns with previous theoretical constraints.

Abstract

This paper revisits the problem of heat conduction in relativistic fluids, associated with issues concerning both stability and causality. It has long been known that the problem requires information involving second order deviations from thermal equilibrium. Basically, any consistent first-order theory needs to remain cognizant of its higher-order origins. We demonstrate this by carrying out the required first-order reduction of a recent variational model. We provide an analysis of the dynamics of the system, obtaining the conditions that must be satisfied in order to avoid instabilities and acausal signal propagation. The results demonstrate, beyond any reasonable doubt, that the model has all the features one would expect of a real physical system. In particular, we highlight the presence of a second sound for heat in the appropriate limit. We also make contact with previous work on the problem by showing how the various constraints on our system agree with previously established results.