Perfect fluidity of a dissipative system: Analytical solution for the Boltzmann equation in $\mathrm{AdS}_{2}\otimes \mathrm{S}_{2}$

TL;DR

This paper analytically solves the relativistic Boltzmann equation for a radially expanding massless gas, revealing conditions under which dissipative systems can exhibit perfect fluidity despite entropy deviations from equilibrium.

Contribution

It provides an exact analytical solution mapping expanding systems to static flows in curved spacetime, highlighting how perfect fluidity can occur with non-equilibrium entropy contributions.

Findings

System exhibits perfect fluid flow despite non-equilibrium entropy density.

Higher order scalar moments account for entropy without affecting energy-momentum.

Analytic expressions for distribution functions and moments are derived.

Abstract

In this paper we obtain an analytical solution of the relativistic Boltzmann equation under the relaxation time approximation that describes the out-of-equilibrium dynamics of a radially expanding massless gas. This solution is found by mapping this expanding system in flat spacetime to a static flow in the curved spacetime $\mathrm{AdS}_{2}\otimes \mathrm{S}_{2}$. We further derive explicit analytic expressions for the momentum dependence of the single particle distribution function as well as for the spatial dependence of its moments. We find that this dissipative system has the ability to flow as a perfect fluid even though its entropy density does not match the equilibrium form. The non-equilibrium contribution to the entropy density is shown to be due to higher order scalar moments (which possess no hydrodynamical interpretation) of the Boltzmann equation that can remain out of equilibrium but do not couple to the energy-momentum tensor of the system. Thus, in this system the slowly moving hydrodynamic degrees of freedom can exhibit true perfect fluidity while being totally decoupled from the fast moving, non-hydrodynamical microscopic degrees of freedom that lead to entropy production.