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Title: Perfect fluidity of a dissipative system: Analytical solution for the Boltzmann equation in AdS2 Ⓧ S2

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 AdS2 Ⓧ S2. 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 nonequilibrium 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. 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:
 [1];  [2]
  1. Columbia Univ., New York, NY (United States); Univ. de Sao Paulo, Sao Paulo (Brazil)
  2. 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)
OSTI Identifier:
1295202
Alternate Identifier(s):
OSTI ID: 1234100
Report Number(s):
BNL-112210-2016-JA
Journal ID: ISSN 1550-7998; 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 1550-7998
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. https://doi.org/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. https://doi.org/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. https://doi.org/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 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 AdS2 Ⓧ S2. 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 nonequilibrium 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. 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}
}

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Cited by: 4 works
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    Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime
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    Analytic Solution of the Boltzmann Equation in an Expanding System
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    Causality and existence of solutions of relativistic viscous fluid dynamics with gravity
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