On the inertia of heat

TL;DR

This paper addresses the controversy over heat inertia in relativistic hydrodynamics, proposing that the inertial term in Eckart's theory results from an inappropriate assumption of constant diffusivity, and that considering space-dependent diffusivity resolves the issue.

Contribution

It introduces the idea that heat diffusivity should be space-dependent in relativistic contexts, clarifying the inertial term controversy in Eckart's heat flux.

Findings

Inertial term arises from assuming constant diffusivity

Space-dependent diffusivity aligns with inhomogeneous media in gravity

Confusion over heat inertia is resolved by redefining diffusivity

Abstract

Does heat have inertia? This question is at the core of a long-standing controversy on Eckart's dissipative relativistic hydrodynamics. Here I show that the troublesome inertial term in Eckart's heat flux arises only if one insists on defining thermal diffusivity as a spacetime constant. I argue that this is the most natural definition, and that all confusion disappears if one considers instead the space-dependent comoving diffusivity, in line with the fact that, in the presence of gravity, space is an inhomogeneous medium.