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## An AdS/CFT Connection between Boltzmann and Einstein

Venue: | Phys.Rev. D81 (2010) 086005, arXiv:0907.1156 [hep-th |

Citations: | 1 - 0 self |

### Citations

5599 | The Large N limit of superconformal field theories and supergravity,” Adv.Theor.Math.Phys
- Maldacena
- 1998
(Show Context)
Citation Context ...y has a smooth future horizon. We also study if irreversibility emerges only at long time scales of observation, unlike the case of the Boltzmann equation. 1 1 INTRODUCTION The AdS/CFT correspondence =-=[1]-=- has opened up new vistas in understanding strongly coupled phenomena in four-dimensional conformal field theories. At strong coupling and large N, the dual classical theory of gravity admits a consis... |

640 |
The Mathematical Theory of Non-uniform Gases
- Chapman, Cowling
- 1970
(Show Context)
Citation Context ...quantity as (δB(2)/B(2)) is a pure number which is smaller than unity (for a proof of this and also for the statement of convergence of such corrections in the context of normal solutions, please see =-=[19, 20]-=-). This result can be translated here, as the normal solutions are just special cases of our conservative solutions and at a sufficiently late time our solutions will be just appropriate normal soluti... |

507 |
The Boltzmann Equation and its Applications,
- Cercignani
- 1988
(Show Context)
Citation Context ...f f will have explicit time-dependent parts which are functionally independent of the hydrodynamic variables. The normal solutions of the Boltzmann equation [18–20] have been extensively discussed in =-=[21]-=-. These solutions can be determined in terms of the five hydrodynamic variables (ρ, ui, p) alone. They describe situations far away from equilibrium, such that observables which vanish at equilibrium ... |

453 | Holographic reconstruction of spacetime and renormalization - Haro, Solodukhin, et al. |

171 |
On the kinetic theory of rarefied gases
- Grad
- 1949
(Show Context)
Citation Context ...tion. In order to keep the proof reasonably self-contained, we give further details on the Boltzmann equation and how one can obtain the hydrodynamic equations seen earlier. We follow the notation of =-=[21,43]-=- mostly for this part of the discussion. This will be followed by the proof in full detail. A.1 A short description of the Boltzmann equation The Boltzmann equation for the one-particle phase space di... |

119 |
On the Dynamical Theory of Gases
- Maxwell
(Show Context)
Citation Context ... SOLUTIONS OF THE BOLTZMANN EQUATION The study of equilibrium and transport properties of dilute gases through the dynamics of one-particle phase space distribution functions was pioneered by Maxwell =-=[14]-=- and further developed by Boltzmann [15] in the 19th century. The Boltzmann equation provides a successful description of nonequilibrium phenomena in rarefied monoatomic gases. It is an equation for t... |

115 |
Asymptotic perfect fluid dynamics as a consequence of Ads/CFT,” Phys
- Janik, Peschanski
- 2006
(Show Context)
Citation Context ...brium states in the universal sector beyond hydrodynamics in a systematic perturbative manner, given that the purely hydrodynamic energy-momentum tensor up to second order in the derivative expansion =-=[7, 12, 13]-=- is known. The plan of the paper is as follows. In Section 2 we outline the conservative solutions in the Boltzmann equation. We then state and investigate our proposal for the regularity condition on... |

95 |
Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen
- Boltzmann
- 1909
(Show Context)
Citation Context ... study of equilibrium and transport properties of dilute gases through the dynamics of one-particle phase space distribution functions was pioneered by Maxwell [14] and further developed by Boltzmann =-=[15]-=- in the 19th century. The Boltzmann equation provides a successful description of nonequilibrium phenomena in rarefied monoatomic gases. It is an equation for the evolution of the one-particle phase s... |

81 | Starinets, “Quasinormal modes and holography
- Kovtun, O
(Show Context)
Citation Context ...hat when the wave vector k vanishes, the frequency ω becomes purely imaginary and equals −iτ−1pi , i.e ω = −iτ−1pi as k → 0. There is however, no such mode in the quasinormal spectrum of black branes =-=[36]-=-. This makes us conclude that λ3 = 1, so that at the linearized level the only solution of (17) is pii j = 0. However, at the nonlinear level we still have nonhydrodynamic solutions given by 2piT (2 −... |

73 | Gravity and Hydrodynamics: Lectures on the fluid-gravity correspondence
- Rangamani
(Show Context)
Citation Context ...tain this universal sector [2]. This universal sector is practically important because it can describe, for instance, hydrodynamics of the dual conformal field theory (for a recent review, please see =-=[4]-=-). However this universal sector, as described by gravity, covers a variety of phenomena well beyond the hydrodynamic regime. Such phenomena also include decoherence [5]. It would then be certainly us... |

63 |
Transport coefficients in high temperature gauge theories. II: Beyond leading log
- Arnold, Moore, et al.
(Show Context)
Citation Context ... can employ the quasiparticle description and also use kinetic theories, which are coarse-grained descriptions of microscopic laws. Specifically, we use the Boltzmann equation which has proven useful =-=[10, 11]-=- in determining the shear viscosity and higher order hydrodynamic transport coefficients and the relaxation time in weakly coupled gauge field theories. It has also been shown that an effective Boltzm... |

54 | Universal hydrodynamics of non-conformal branes - Kanitscheider, Skenderis |

42 | Viscous hydrodynamics relaxation time from AdS/CFT, Phys - Heller, Janik |

38 | Universal holographic hydrodynamics at finite coupling,” - Buchel, Myers, et al. - 2008 |

24 |
Kaluza-Klein holography
- Skenderis, Taylor
- 2006
(Show Context)
Citation Context ...mensional equations of motion. There is no guarantee of a consistent truncation to pure gravity anymore. However, we can use holographic renormalization with Kaluza-Klein reduction to five dimensions =-=[31]-=- to argue that we can readily extend the solutions in the universal sector, perturbatively in the string tension (≈ 1/√λ in appropriate units) and string coupling (whose N dependence is 1/N). This can... |

14 |
Dissipative hydrodynamics and heavy ion collisions, Phys
- Baier, Romatschke, et al.
(Show Context)
Citation Context ... can employ the quasiparticle description and also use kinetic theories, which are coarse-grained descriptions of microscopic laws. Specifically, we use the Boltzmann equation which has proven useful =-=[10, 11]-=- in determining the shear viscosity and higher order hydrodynamic transport coefficients and the relaxation time in weakly coupled gauge field theories. It has also been shown that an effective Boltzm... |

12 | On the universal hydrodynamics of strongly coupled CFTs with gravity duals - Gupta, Mukhopadhyay |

12 | Second order hydrodynamic coefficients from kinetic theory,” Phys - York, Moore |

12 |
Early collective expansion: relativistic hydrodynamics and the transport properties of QCD matter,”
- Heinz
- 2010
(Show Context)
Citation Context ...t the Relativistic Heavy Ion Collider (RHIC) suggest that the evolution of quark-gluon plasma (QGP) can be well approximated by hydrodynamic equations, very soon after its formation from the fireball =-=[30]-=-. Given that the perturbative nonequilibrium dynamics of hot QCD for temperatures greater than the microscopic scale Λ is equivalent to a relativistic semiclassical Boltzmann equation [10], we know pe... |

10 |
théorie statistique des fluides et l’équation d’état
- Yvon, La
- 1935
(Show Context)
Citation Context ...equation, though an appropriate averaging over the environmental degrees of freedom is required to get the final equilibrium configuration. 11 To begin with, consider the BBGKY heirarchy of equations =-=[28]-=- which describes a hierarchy of coupled semiclassical nonrelativistic equations for the evolution of multiparticle phase space distributions. This hierarchy is useful for developing kinetic theory of ... |

9 |
Speeds of propagation in classical and relativistic extended thermodynamics,” Living Rev
- Muller
- 1999
(Show Context)
Citation Context ...classical Boltzmann equation at sufficiently late times can be approximated by an appropriate conservative solution, since the maximum speed of propagation of linearized modes increases monotonically =-=[27]-=- as more and more higher moments are included. 2.3 Multicomponent systems So far we have pretended as if our system is composed of only one component or particle. However gauge theories have many spec... |

8 | Entropy Current in Conformal Hydrodynamics
- Loganayagam
(Show Context)
Citation Context ...lack-brane solutions, which by our logic should constitute the normal or purely hydrodynamic solutions at large N and strong coupling, indeed demonstrate the existence of a family of entropy currents =-=[38]-=-. However, unlike for the normal solutions of the Boltzmann equation, or in the IsraelStewart-Muller formalism, these entropy currents are not of the form suµ, where s could be interpreted as the none... |

4 |
Nonstationary irreversible thermodynamics: A causal relativistic theory”,Annals of Physics 100 310
- Müller, Physik
- 1967
(Show Context)
Citation Context ...gMills theory. Moreover an entropy current cannot be probably constructed beyond the class of purely hydrodynamic solutions, hence we cannot use any formalism like the Israel-Stewart-Muller formalism =-=[32]-=- to guess an equation for piµν. This is 15 because we should not expect a monotonic approach to equilibrium, as in the case of the Boltzmann equation, when we go to the exact microscopic description [... |

2 |
Phys Rev A 76, 053607 (2007) [arxiv: 0707.1520
- Rupak, Schäfer
(Show Context)
Citation Context ...corrections as well [25]. One has to employ the Sonine polynomials, which are generalizations of Hermite polynomials, to find solutions of the required algebraic solutions of the higher moments as in =-=[26]-=-. The main objection could be that for the proof of existence of solutions, we use a theorem due to Hilbert which is explicitly stated for the nonrelativistic classical J. However the details are exac... |

1 |
the purely hydrodynamic context of ”tubewise black-brane solutions,” the Israel-Stewart-Muller formalism is not valid. This has been discussed with references later in the text
- in
(Show Context)
Citation Context ...] to guess an equation for piµν. This is 15 because we should not expect a monotonic approach to equilibrium, as in the case of the Boltzmann equation, when we go to the exact microscopic description =-=[33]-=-. The safest strategy therefore, will be to use only the following basic inputs without resorting to guesswork. • The first input is that the equation for piµν has to be conformally covariant because ... |

1 |
Starinets for discussion on this point
- O
(Show Context)
Citation Context ...ot present. However, we know that the quasinormal modes have infinite branches of higher overtones other than the 19 hydrodynamic sound and shear branches. This naive comparison is somewhat misplaced =-=[37]-=- because, as we know, nonlinearities do affect linearized propagation in quantum field theories. Since our equations are actually equivalent to the nonequilibrium field theory equation of motion of th... |

1 |
for the hydrodynamic variables, the action of the subdivisions of the time derivative on them could have been treated as unknowns. But we have chosen the logically equivalent path of declaring them beforehand from our experience with the case of normal so
- Even
(Show Context)
Citation Context ...ct on p(nh)i j , we have defined the time derivative. Indeed, we have to solve for the action of the time-derivative because specifying this amounts to proving the existence of conservative solutions =-=[41]-=-. 29 3. The next thing is to note that the full shear-stress tensor pi j (just like any other higher moment) has an expansion in both and δ. If we denote δpi j = pi j − p(nh)i j , then for n ≥ 1 δp(... |