Entropy production in simple special relativistic fluids

Abstract

It is well known that, in the absence of external forces, simple non-relativistic uids involve entropy production only through heat conduction and shear viscosity [1]. In this work, it is shown that a number density gradient contributes to the local entropy production of a simple relativistic uid using special relativistic kinetic theory. Also, the presence of an external eld may cause strictly relativistic contributions to the entropy production, a fact not widely recognized. The implications of these e ects are thoroughly discussed.

The Energy-Momentum Tensor in Relativistic Kinetic Theory: The Role of the Center of Mass Velocity in the Transport Equations for Multicomponent Mixtures

“…The invariant velocity element included in Eqs. (24) and (25) has been discussed by many authors since the original works by Jüttner, and a brief calculation leading to its explicit form is included in the appendix of reference [6]. The total balance equations are obtained summing over all species, leading to the expressions:…”

“…( 21) by k B ln f (i) and integration with respect to the invariant measure d * V (i) . The corresponding result reads [25]:…”

“…( 35) in Appendix B of Ref. [25]). In Table 1 we compare both descriptions of relativistic kinetic theory in terms of the aforementioned operational definitions of the center of mass velocity of the relativistic mixture.…”