a b s t r a c tIn this paper we show how using a relativistic kinetic equation the ensuing expression for the heat flux can be cast in the form required by Classical Irreversible Thermodynamics. Indeed, it is linearly related to the temperature and number density gradients and not to the acceleration as the so called ''first order in the gradients'' theories propose. Since the specific expressions for the transport coefficients are irrelevant for our purposes, the BGK form of the kinetic equation is used. Moreover, from the resulting hydrodynamic equations it is readily seen that the equilibrium state is stable in the presence of the spontaneous fluctuations in the transverse hydrodynamic velocity mode of the simple relativistic fluid. The implications of this result are thoroughly discussed.

It is shown that the so-called generic instabilities that appear in the framework of relativistic linear irreversible thermodynamics (LIT), describing the fluctuations of a simple fluid close to equilibrium, arise due to the coupling of heat with hydrodynamic acceleration which appears in Eckart's formalism of relativistic irreversible thermodynamics. Further, we emphasize that such behavior should be interpreted as a contradiction to the postulates of LIT, namely a violation of Onsager's hypothesis on the regression of fluctuations, and not as fluid instabilities. Such contradictions can be avoided within a relativistic linear framework if a Meixner-like approach to the phenomenological equations is employed.

In this paper we calculate the Rayleigh-Brillouin spectrum for a relativistic simple fluid according to three different versions available for a relativistic approach to nonequilibrium thermodynamics. An outcome of these calculations is that Eckart's version predicts that such spectrum does not exist. This provides an argument to question its validity. The remaining two results, which differ one from another, do provide a finite form for such spectrum. This raises the rather intriguing question as to which of the two theories is a better candidate to be taken as a possible version of relativistic nonequilibrium thermodynamics. The answer will clearly require deeper examination of this problem.

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According to standard thermophysical theories, cross effects are mostly present in multicomponent systems. In this paper we show that for relativistic fluids an electric field generates a heat flux even in the single component case. In the non-relativistic limit the effect vanishes and Fourier's law is recovered. This result is novel and may have applications in the transport properties of very hot plasmas.Comment: Paper submitted to the Journal of Non-Equilibrium Thermodynamic