Reversible dissipative processes, conformal motions and Landau damping

Abstract

The existence of a dissipative flux vector is known to be compatible with reversible processes, provided a timelike conformal Killing vector (CKV) χ α = V α T (where V α and T denote the fourvelocity and temperature respectively) is admitted by the space-time. Here we show that if a constitutive transport equation, either within the context of standard irreversible thermodynamics or the causal Israel-Stewart theory, is adopted, then such a compatibility also requires vanishing dissipative fluxes. Therefore, in this later case the vanishing of entropy production generated by the existence of such CKV is not actually associated to an imperfect fluid, but to a non-dissipative one. We discuss also about Landau damping.

Relativistic shear-free fluids with symmetry

“…These examples illustrate the applications of conformal motions in cosmology. Mak and Harko [14] studied charged strange stars with a quark equation of state, Esculpi and Aloma [15] generated anisotropic relativistic charged fluid spheres with a linear barotropic equation of state, Usmani et al [16] extended the concept of a Bose-Einstein condensate to gravity to construct gravastars and Herrera et al [17] studied reversible dissipative processes and Landau damping in stellar systems. These examples are a sample of the various applications of conformal motions in relativistic astrophysics.…”

Non-Perfect-Fluid Space-Times in Thermodynamic Equilibrium and Generalized Friedmann Equations

“…This view is reinforced by the results obtained in [19]. There, it was shown that in conformstationary models the heat-flux must vanish for zero anisotropic pressure and under the assumption of a heat-flux law of the Israel-Stewart type.…”

“…There, it was shown that in conformstationary models the heat-flux must vanish for zero anisotropic pressure and under the assumption of a heat-flux law of the Israel-Stewart type. An example for physical processes in which this does not hold (Landau damping) is also provided in [19].…”

The Gibbs Paradox, the Landauer Principle and the Irreversibility Associated with Tilted Observers

“…In other words, even if ab initio the fluid is assumed to be imperfect (non-vanishing heat flow vector), the imposition of the CKV and the vanishing entropy production condition may cancel the heat flux once a transport equation is assumed (see [36] for a detailed discussion on this point).…”

“…However, a much more carefull analysis of the problem readily shows, that the compatibility of reversible processes and the existence of dissipative fluxes becomes trivial if a constitutive transport equation is adopted, since in this latter case such compatibility forces the heat flux vector to vanish as well. In other words, even if ab initio the fluid is assumed imperfect (nonvanishing heat flow vector) the imposition of the CKV and the vanishing entropy production condition may cancel the heat flux, once a transport equation is assumed (see [36] for a detailed discussion on this point).…”