# An Axiomatic Review of Israel-Stewart Hydrodynamics and Extended Irreversible Thermodynamics

## TL;DR

This paper reviews the axiomatic foundations of Israel-Stewart hydrodynamics and Extended Irreversible Thermodynamics (EIT), highlighting their applicability to relativistic dissipative phenomena and limitations in describing optically thin radiative transfer.

## Contribution

It provides an axiomatic review of EIT and Israel-Stewart theory, clarifying their scope and limitations, especially regarding radiative transfer in optically thin media.

## Key findings

- EIT is applicable to radiative transfer in optically thick media.
- EIT cannot describe radiative transfer in optically thin media due to photon non-self-interaction.
- The breakdown of EIT in optically thin situations is explicitly explained.

## Abstract

The causality of dissipative phenomena can not be treated in traditional theories of dissipations, Fourier laws and Navier-Stokes equations. This is the reason why the dissipative phenomena have not been studies well in relativistic situations. Furthermore, the interactions among dissipations, e.g. the heating of fluid due to viscous flow and the occurrence of viscous flow due to heat flux, are not explicitly described in those traditional laws. One of the phenomenologies which describe the causality and interaction of dissipations is the Extended Irreversible Thermodynamics (EIT). (Israel-Stewart theory of dissipative hydrodynamics is one approximate form of EIT.) This manuscript reviews an axiomatic construction of EIT and Israel-Stewart hydrodynamic theory. Also, we point out that the EIT is also applicable to radiative transfer in optically \emph{thick} matters. However, radiative transfer in optically \emph{thin} matters can not be described by EIT, because the non-self-interacting nature of photons is incompatible with a basic requirement of EIT, "the bilinear form of entropy production rate". The break down of EIT in optically thin situation is not explicitly recognized in standard references of EIT and Israel-Stewart theory. Some detail of how EIT fails to describe a radiative transfer in optically thin situations is also explained. (This manuscript is a revision of the contribution to a book Ref.[26] published in 2011. So, recent developments made after 2011 may not be cited.)