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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.

In this paper we show how an extension of the nonequilibrium-statistical-operator method, relying upon the maximum-entropy principle set up by Jaynes [Am. J. Phys. 33, 391 (1965)], may be used to describe the time evolution of an arbitrary many-body system. The Gibbs space of the observables describing the macrostates of the system is extended to include not only the conserved variables, but additional ones whose origin is directly related to the microscopic nature of the system manifested in its Hamiltonian. This allows us to go beyond linear irreversible thermodynamics and enter into the domain of what is now known as extended irreversible thermodynamics (EIT). Transport equations for the extended basic set of macrovariables are derived, showing that the Maxwell-Cattaneo-Vernotte equations of EIT are obtained. The relaxation times and transport coefFicients contained therein can be calculated from the microscopic dynamics of the system averaged over an appropriate nonequilibrium coarse-grained probability density. Other outstanding features of the methods are emphasized and related to already-established results for nonequilibrium systems.