Reversible Dissipative Processes, Conformal Motions and Landau Damping

TL;DR

This paper explores the conditions under which dissipative fluxes can coexist with reversible processes in spacetime, revealing that certain conformal symmetries imply non-dissipative behavior and discussing implications for Landau damping.

Contribution

It demonstrates that the presence of a conformal Killing vector constrains dissipative fluxes, linking symmetry properties to the non-dissipative nature of fluids in thermodynamics.

Findings

Dissipative fluxes vanish when a conformal Killing vector is present with certain thermodynamic conditions.

Compatibility of dissipative fluxes with reversible processes requires specific spacetime symmetries.

Landau damping is discussed in relation to conformal motions and dissipative processes.

Abstract

The existence of a dissipative flux vector is known to be compatible with reversible processes, provided a timelike conformal Killing vector (CKV) $\chi^\alpha=\frac{V^\alpha}{T}$ (where $V^\alpha$ and $T$ denote the four-velocity 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.