Ana Laura García-Perciante

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.

On the kinetic foundations of Kaluza's magnetohydrodynamics

Abstract Recent work has shown the existence of a relativistic effect present in a single component non-equilibrium fluid, corresponding to a heat flux due to an electric field [J. Non-Equilib. Thermodyn. 38 (2013), 141–151]. The treatment in that work was limited to a four-dimensional Minkowski space-time in which the Boltzmann equation was treated in a special relativistic approach. The more complete framework of general relativity can be introduced to kinetic theory in order to describe transport processes associated to electromagnetic fields. In this context, the original Kaluzas formalism is a promising approach [Sitz. Ber. Preuss. Akad. Wiss. (1921), 966–972; Gen. Rel. Grav. 39 (2007), 1287–1296; Phys. Plasmas 7 (2000), 4823–4830]. The present work contains a kinetic theory basis for Kaluzas magnetohydrodynamics and gives a novel description for the establishment of thermodynamic forces beyond the special relativistic description.

Hyperbolic heat equation in Kaluza's magnetohydrodynamics

This paper shows that a hyperbolic equation for heat conduction can be obtained directly using the tenets of linear irreversible thermodynamics in the context of the five dimensional space-time metric originally proposed by T. Kaluza back in 1922. The associated speed of propagation is slightly lower than the speed of light by a factor inversely proportional to the specific charge of the fluid element. Moreover, consistency with the second law of thermodynamics is achieved. Possible implications in the context of physics of clusters of galaxies of this result are suggested.

Entropy production in simple special relativistic fluids

It is well known that, in the absence of external forces, simple non-relativistic fluids involve entropy production only through heat conduction and shear viscosity. In this work, it is shown that a number density gradient contributes to the local entropy production of a simple relativistic fluid using special relativistic kinetic theory. Also, the presence of an external field may cause strictly relativistic contributions to the entropy production, a fact not widely recognized. The implications of these effects are thoroughly discussed.

Rotational Viscosity in Linear Irreversible Thermodynamics and its Application to Neutron Stars

Abstract A generalized analysis of the local entropy production of a simple fluid is used to show that, if intrinsic angular momentum is taken into account, rotational viscosity must arise in the linear non-equilibrium regime. As a consequence, the stress tensor of dense rotating matter, such as the one present in neutron stars, posseses a significant non-vanishing antisymmetrical part. A simple argument suggests that, due to the extreme magnetic fields present in neutron stars, the relaxation time associated to rotational viscosity is large (∼1021). The formalism leads to generalized Navier-Stokes equations useful in neutron star physics which involve vorticity in the linear regime.

Kaluza’s theory in generalized coordinates

Maxwell’s equations can be obtained in generalized coordinates by considering the electromagnetic field as an external agent. The work presented here shows how to obtain the electrodynamics for a charged particle in generalized coordinates eliminating the concept of external force. Based on Kaluza’s formalism, the one presented here extends the 5×5 metric into a 6×6 space–time giving enough room to include magnetic monopoles in a very natural way.

Relativistic Heat Flux for a Single Component Charged Fluid in the Presence of an Electromagnetic Field

Abstract Transport properties in gases are significantly affected by temperature. In previous works it has been shown that when the thermal agitation in a gas is sufficient for relativistic effects to become relevant, heat dissipation is driven not solely by a temperature gradient but also by other vector forces. In the case of relativistic charged fluids, a heat flux is driven by an electrostatic field even in the single species case. The present work generalizes such result by considering also a magnetic field in an arbitrary reference frame. The corresponding constitutive equation is explicitly obtained showing that both electric and magnetic forces contribute to thermal dissipation. This result may lead to relevant effects in plasma dynamics.

Thermoelectric and Thermomagnetic Effects in Kaluza’s Kinetic Theory

Abstract A five-dimensional treatment of the Boltzmann equation is used to establish the constitutive equations that relate thermodynamic fluxes and forces up to first order in the gradients for simple charged fluids in the presence of electromagnetic fields. The formalism uses the ansatz first introduced by Kaluza back in 1921, proposing that the particle charge–mass ratio is proportional to the fifth component of its velocity field. It is shown that in this approach, space–time curvature yields thermodynamic forces leading to generalizations of the well-known cross-effects present in linear irreversible thermodynamics.

Gravitational Contribution to the Heat Flux in a Simple Dilute Fluid: An Approach Based on General Relativistic Kinetic Theory to First Order in the Gradients

Richard C. Tolman analyzed the relation between a temperature gradient and a gravitational field in an equilibrium situation. In 2012, Tolman’s law was generalized to a non-equilibrium situation for a simple dilute relativistic fluid. The result in that scenario, obtained by introducing the gravitational force through the molecular acceleration, couples the heat flux with the metric coefficients and the gradients of the state variables. In the present paper it is shown, by explicitly describing the single particle orbits as geodesics in Boltzmann’s equation, that a gravitational field drives a heat flux in this type of system. The calculation is devoted solely to the gravitational field contribution to this heat flux in which a Newtonian limit to the Schwarzschild metric is assumed. The corresponding transport coefficient, which is obtained within a relaxation approximation, corresponds to the dilute fluid in a weak gravitational field. The effect is negligible in the non-relativistic regime, as evidenced by the direct evaluation of the corresponding limit.

Two temperature gas equilibration model with a Fokker-Planck type collision operator

The equilibration process of a binary mixture of gases with two different temperatures is revisited using a Fokker-Planck type equation. The collision integral term of the Boltzmann equation is approximated by a Fokker-Planck differential collision operator by assuming that one of the constituents can be considered as a background gas in equilibrium while the other species diffuses through it. As a main result the coefficients of the linear term and of the first derivative are modified by the temperature and kinetic energy difference of the two species. These modifications are expected to influence the form of the solution for the distribution function and the corresponding transport equations. When temperatures are equal, the usual result of a Rayleigh gas is recovered.