Perfect fluidity of a dissipative system: Analytical solution for the Boltzmann equation in AdS_{2} Ⓧ S_{2}
Abstract
In this paper we obtain an analytical solution of the relativistic Boltzmann equation under the relaxation time approximation that describes the outofequilibrium 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 AdS_{2} Ⓧ S_{2}. We further derive explicit analytic expressions for the momentum dependence of the singleparticle 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 nonequilibrium contribution to the entropy density is shown to be due to higherorder scalar moments (which possess no hydrodynamical interpretation) of the Boltzmann equation that can remain out of equilibrium but do not couple to the energymomentum tensor of the system. Furthermore, in this system the slowly moving hydrodynamic degrees of freedom can exhibit true perfect fluidity while being totally decoupled from the fast moving, nonhydrodynamical microscopic degrees of freedom that lead to entropy production.
 Authors:

 Columbia Univ., New York, NY (United States); Univ. de Sao Paulo, Sao Paulo (Brazil)
 McGill Univ., Montreal, QC (Canada); Brookhaven National Lab. (BNL), Upton, NY (United States)
 Publication Date:
 Research Org.:
 Brookhaven National Lab. (BNL), Upton, NY (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Nuclear Physics (NP) (SC26)
 OSTI Identifier:
 1295202
 Alternate Identifier(s):
 OSTI ID: 1234100
 Report Number(s):
 BNL1122102016JA
Journal ID: ISSN 15507998; R&D Project: KB0301020; KB0301020
 Grant/Contract Number:
 SC00112704; SC0012704
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physical Review. D, Particles, Fields, Gravitation and Cosmology
 Additional Journal Information:
 Journal Volume: 92; Journal Issue: 11; Journal ID: ISSN 15507998
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 73 NUCLEAR PHYSICS AND RADIATION PHYSICS
Citation Formats
Noronha, Jorge, and Denicol, Gabriel S. Perfect fluidity of a dissipative system: Analytical solution for the Boltzmann equation in AdS2 Ⓧ S2. United States: N. p., 2015.
Web. doi:10.1103/PhysRevD.92.114032.
Noronha, Jorge, & Denicol, Gabriel S. Perfect fluidity of a dissipative system: Analytical solution for the Boltzmann equation in AdS2 Ⓧ S2. United States. doi:10.1103/PhysRevD.92.114032.
Noronha, Jorge, and Denicol, Gabriel S. Wed .
"Perfect fluidity of a dissipative system: Analytical solution for the Boltzmann equation in AdS2 Ⓧ S2". United States. doi:10.1103/PhysRevD.92.114032. https://www.osti.gov/servlets/purl/1295202.
@article{osti_1295202,
title = {Perfect fluidity of a dissipative system: Analytical solution for the Boltzmann equation in AdS2 Ⓧ S2},
author = {Noronha, Jorge and Denicol, Gabriel S.},
abstractNote = {In this paper we obtain an analytical solution of the relativistic Boltzmann equation under the relaxation time approximation that describes the outofequilibrium 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 AdS2 Ⓧ S2. We further derive explicit analytic expressions for the momentum dependence of the singleparticle 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 nonequilibrium contribution to the entropy density is shown to be due to higherorder scalar moments (which possess no hydrodynamical interpretation) of the Boltzmann equation that can remain out of equilibrium but do not couple to the energymomentum tensor of the system. Furthermore, in this system the slowly moving hydrodynamic degrees of freedom can exhibit true perfect fluidity while being totally decoupled from the fast moving, nonhydrodynamical microscopic degrees of freedom that lead to entropy production.},
doi = {10.1103/PhysRevD.92.114032},
journal = {Physical Review. D, Particles, Fields, Gravitation and Cosmology},
number = 11,
volume = 92,
place = {United States},
year = {2015},
month = {12}
}
Web of Science