While the synthetic treatment of the foregoing sections is concise and seems quite elegant, it is also little suggestive of the laws for heat flux and stress that we associate with non-equilibrium thermodynamics. Moreover, the elegance of this treatment disguises the fact that much work is needed in order to obtain specific results.

The following section highlights this situation by considering a viscous heat-conducting gas, a material which is fully characterized by 14 fields, viz. the density and flux of mass, energy and momentum, and stress and heat flux. With this choice of fields we shall be able to exploit the principle of relativity and the entropy inequality in explicit form and to calculate some specific pulse speeds.

It is true that much of the rigorous formal structure of the preceding section is lost when it comes to specific calculations. Linearization around equilibrium cannot be avoided, if we wish to obtain specific results, and that destroys global invertibility and general symmetric hyperbolicity. These properties are now restricted to situations close to equilibrium.

5.1 Thermodynamic processes in viscous, heat-conducting gases

5.2 Constitutive theory

5.3 Results of the constitutive theory

5.4 The laws of Navier–Stokes and Fourier

5.5 Specific results for a non-degenerate relativistic gas

5.6 Characteristic speeds in a viscous, heat-conducting gas

5.7 Discussion

5.2 Constitutive theory

5.3 Results of the constitutive theory

5.4 The laws of Navier–Stokes and Fourier

5.5 Specific results for a non-degenerate relativistic gas

5.6 Characteristic speeds in a viscous, heat-conducting gas

5.7 Discussion

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