Alfredo Sandoval-Villalbazo

On the nature of the so-called generic instabilities in dissipative relativistic hydrodynamics

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.

Relativistic non-equilibrium thermodynamics revisited

Abstract Relativistic irreversible thermodynamics is reformulated following the conventional approach proposed by Meixner in the non-relativistic case. Clear separation between mechanical and non-mechanical energy fluxes is made. The resulting equations for the entropy production and the local internal energy have the same structure as the non-relativistic ones. Assuming linear constitutive laws, it is shown that consistency is obtained both with the laws of thermodynamics and causality.

Relativistic transport theory for simple fluids to first order in the gradients

In 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.

Meixner-Prigogine scheme in relativistic transport theory

Meixner-Prigogine scheme of linear non-equilibrium thermodynamics is reproduced for the first time within the framework of general relativity for static space-times. Heat and motion equations are built using two fundamental assumptions: conservation laws are true, and local thermodynamical equilibrium hypothesis holds. This is done introducing the heat flow four vector following the procedure used in the Meixner-Prigogine theory of irreversible thermodynamics, instead of placing it in the stress energy tensor (which is the commonly accepted approach for the problem). Further study of the transport coefficients and the structure of the transport equations here established will be left for future work.

Rayleigh-Brillouin spectrum in special relativistic hydrodynamics

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 Eckarts 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.

The relativistic kinetic formalism revisited

The relativistic Boltzmann equation is used to provide microscopical support to the relativistic Meixner–Prigogine scheme of linear irreversible thermodynamics. A suitable form of the chaotic velocities is employed in order to construct expressions for the total energy four-flux and the pressure tensor, a method that is not used in current approaches to the subject. The non-relativistic equations are shown to be satisfied within this formalism, and important cosmological implications of the theory, such as a modification of the expansion rate in Robertson–Walker–Friedman Universes are finally examined.

Relativistic Navier-Stokes equations in the Meixner-Prigogine scheme

Viscous effects are included in the relativistic Meixner-Prigogine scheme (see: A. Sandoval-Villalbazo, L.S. Garcia-Colin, Physica A 234 (1996) 358). A relativistic generalization of the Navier-Stokes equations is obtained within this framework. The system obtained is analyzed and compared with related work.

Generalized relativistic Chapman–Enskog solution of the Boltzmann equation

The Chapman–Enskog method of solution of the relativistic Boltzmann equation is generalized in order to admit a time-derivative term associated to a thermodynamic force in its first order solution. Both existence and uniqueness of such a solution are proved based on the standard theory of integral equations. The mathematical implications of the generalization introduced here are thoroughly discussed regarding the nature of heat as chaotic energy transfer in the context of relativity theory.

Relativistic magnetohydrodynamics revisited

Magnetohydrodynamics is discussed within the framework of irreversible thermodynamics. The nonrelativistic version is reviewed by introducing the electromagnetic field as an external force. Results are discussed and emphasis is placed on the fact that the transport equations, being of a parabolic type, violate causality. The relativistic version is next considered using Kaluza’s ideas about unifying fields in terms of the corresponding space–time curvature for a given metric. The outcome of this approach is rewarding. The conservation equations follow in a direct way as well as the entropy balance equation with an entropy production whose form suggests the type of constitutive equations that are consistent with its semipositive character. Further, the resulting transport equations are of a hyperbolic type in agreement with causality. Therefore, relativistic magnetohydrodynamics is placed within a thermodynamic framework consistent with the second law.

Benedicks effect in a relativistic simple fluid

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 Fouriers law is recovered. This result is novel and may have applications in the transport properties of very hot plasmas.