Internal energy in dissipative relativistic fluids

TL;DR

This paper extends the theory of relativistic fluids by including momentum density in the state space, showing that internal energy must account for both energy and momentum densities to satisfy thermodynamic principles.

Contribution

It introduces an extended relativistic fluid model where the state space includes momentum density, providing new constitutive relations consistent with thermodynamics.

Findings

Energy depends on energy density and momentum density in a specific way

Local rest frame energy density is not the sole internal energy

Derived constitutive relations for stress and energy flux

Abstract

Liu procedure is applied to a first order weakly nonlocal special relativistic fluid. It is shown, that a reasonable relativistic theory is and extended one, where the basic state space contains the momentum density. This property follows from the structure of the energy-momentum balance and the Second Law of thermodynamics. Moreover, the entropy depends on the energy density and the momentum density on a given specific way, indicating that the local rest frame energy density cannot be interpreted as the internal energy, the local rest frame momentum density should be considered, too. The corresponding constitutive relations for the stress and the energy flux are derived.