It has recently been shown that the Einstein equation can be derived by demanding a non-equilibrium entropy balance law dS = dQ/T + dS_i hold for all local acceleration horizons through each point in spacetime. The entropy change dS is proportional to the change in horizon area while dQ and T are the energy flux across the horizon and Unruh temperature seen by an accelerating observer just inside the horizon. The internal entropy production term dS_i is proportional to the squared shear of the horizon and the ratio of the proportionality constant to the area entropy density is \hbar/4π. Here we will show that this derivation can be reformulated in the language of hydrodynamics. We postulate that the vacuum thermal state in the Rindler wedge of spacetime obeys the holographic principle. Hydrodynamic perturbations of this state exist and are manifested in the dynamics of a stretched horizon fluid at the horizon boundary. Using the equations of hydrodynamics we derive the entropy balance law and show the Einstein equation is a consequence of vacuum hydrodynamics. This result implies that \hbar/4πis the shear viscosity to entropy density ratio of the local vacuum thermal state. The value \hbar/4πhas attracted much attention as the shear viscosity to entropy density ratio for all gauge theories with an Einstein gravity dual. It has also been conjectured as the universal lower bound on the ratio. We argue that our picture of the vacuum thermal state is consistent with the physics of the gauge/gravity dualities and then consider possible applications to open questions.
We show that relativistic hydrodynamics in Minkowski space-time has intrinsic ambiguity in second order viscosity parameters in the Landau-Lifshitz frame. This stems from the possibility of improvements of energy-momentum tensor. There exist at least two viscosity parameters which can be removed by using this ambiguity in scale invariant hydrodynamics in (1+3) dimension, and seemingly non-conformal hydrodynamic theories can be hiddenly conformal invariant.
In (2+1)-dimensional hydrodynamic systems with broken parity, the shear and bulk viscosity is joined by the Hall viscosity and curl viscosity. The dual holographic model has been constructed by coupling a pseudo scalar to the gravitational Chern-Simons term in (3+1)-dimensional bulk gravity. In this paper, we investigate the non-relativistic fluid with Hall viscosity and curl viscosity living on a finite radial cutoff surface in the bulk. Employing the non-relativistic hydrodynamic expansion method, we obtain the incompressible Navier-Stokes equations with Hall viscosity and curl viscosity. Un…
Hydrodynamics predicts long-lived sound and shear waves. Thermal fluctuations in these waves can lead to the diffusion of momentum density, contributing to the shear viscosity and other transport coefficients. Within viscous hydrodynamics in 3+1 dimensions, this leads to a positive contribution to the shear viscosity, which is finite but inversely proportional to the microscopic shear viscosity. Therefore the effective infrared viscosity is bounded from below. The contribution to the second-order transport coefficient $τ_π$ is divergent, which means that second-order relativistic viscous hydro…
Hydro-kinetic theory of thermal fluctuations is applied to a non-conformal relativistic fluid. Solving the hydro-kinetic equations for an isotropically expanding background we find that hydrodynamic fluctuations give ultraviolet divergent contributions to the energy-momentum tensor. After shifting the temperature to account for the energy of non-equilibrium modes, the remaining divergences are renormalized into local parameters, e.g. pressure and bulk viscosity. We also confirm that the renormalization of the pressure and bulk viscosity is universal by computing them for a Bjorken expansion. T…
We compute the bulk viscosity in holographic models dual to theories with Lifshitz scaling and/or hyperscaling violation, using a generalization of the bulk viscosity formula derived in arXiv:1103.1657 from the null focusing equation. We find that only a class of models with massive vector fields are truly Lifshitz scale invariant, and have a vanishing bulk viscosity. For other holographic models with scalars and/or massless vector fields we find a universal formula in terms of the dynamical exponent and the hyperscaling violation exponent.
We solve second order relativistic hydrodynamics equations for a boost-invariant 1+1-dimensional expanding fluid with an equation of state taken from lattice calculations of the thermodynamics of strongly coupled quark-gluon plasma. We investigate the dependence of the energy density as a function of proper time on the values of the shear viscosity, the bulk viscosity, and second order coefficients, confirming that large changes in the values of the latter have negligible effects. Varying the shear viscosity between zero and a few times s/(4 pi), with s the entropy density, has significant eff…
The shear viscosity coefficient and the corresponding relaxation time for causal dissipative hydrodynamics are calculated based on the microscopic formula proposed in [T. Koide and T. Kodama, Phys. Rev. \textbf{E 78}, 051107 (2008)]. Here, the exact formula is transformed into a more compact form and applied it to evaluate these transport coefficients in the chiral perturbation theory and perturbative QCD. It is shown that in the leading order calculation, the causal shear viscosity coefficient $η$ reduces to that of the ordinary Green-Kubo-Nakano formula, and the relaxation time $τ_π$ is rela…
Kovtun, Son and Starinets have conjectured that the viscosity to entropy density ratio $η/s$ is always bounded from below by a universal multiple of $\hbar$ i.e., $\hbar/(4πk_{B})$ for all forms of matter. Mysteriously, the proposed viscosity bound appears to be saturated in all computations done whenever a supergravity dual is available. We consider the near horizon limit of a stack of M2-branes in the grand canonical ensemble at finite R-charge densities, corresponding to non-zero angular momentum in the bulk. The corresponding four-dimensional R-charged black hole in Anti-de Sitter space pr…
Second-order dissipative hydrodynamic equations for each component of a multi-component system are derived using the entropy principle. Comparison of the solutions with kinetic transport results demonstrates validity of the obtained equations. We demonstrate how the shear viscosity of the total system can be calculated in terms of the involved cross sections and partial densities. Presence of the inter-species interactions leads to a characteristic time-dependence of the shear viscosity of the mixture, which also means that the shear viscosity of a mixture cannot be calculated using the Green-…
The derivation of Lifshitz-invariant hydrodynamics from holography, presented in [arXiv:1508.02494] is generalized to arbitrary hyperscaling violating Lifshitz scaling theories with an unbroken U(1) symmetry. The hydrodynamics emerging is non-relativistic with scalar "forcing". By a redefinition of the pressure it becomes standard non-relativistic hydrodynamics in the presence of specific chemical potential for the mass current. The hydrodynamics is compatible with the scaling theory of Lifshitz invariance with hyperscaling violation. The bulk viscosity vanishes while the shear viscosity to en…
In this paper we consider a metric with hyperscaling violation on black brane background. In this background we calculate the ratio of shear viscosity to entropy density with hydrodynamics information. The calculation of this quantity lead us to constraint $θ$ as $3\leqθ<4$, and $θ\leq0$. In that case we show that the quantity of $\fracη{s}$ not dependent to hyperscaling violation parameter $θ.$ Our results about ratio of shear viscosity to entropy density in direct of $QCD$ point of view agree with other works in literature as $1/4π$.
We study the hydrodynamic properties of strongly coupled SU(N) Yang-Mills theory of the D1-brane at finite temperature in the framework of gauge/gravity duality. The only non-trivial viscous transport coefficient in 1+1 dimensions is the bulk viscosity. We evaluate the bulk viscosity by isolating the quasi-normal mode corresponding to the sound channel for the gravitational background of the D1-brane. We find that the ratio of the bulk viscosity to the entropy density to be 1/4π. This ratio continues to be $1/4π$ also in the regime when the D1-brane Yang-Mills theory is dual to the gravitation…
With the goal of deriving dissipative hydrodynamics from an action, we study classical actions for open systems, which follow from the generic structure of effective actions in the Schwinger-Keldysh Closed-Time-Path formalism with two time axes and a doubling of degrees of freedom. The central structural feature of such effective actions is the coupling between degrees of freedom on the two time axes. This reflects the fact that from an effective field theory point of view, dissipation is the loss of energy of the low-energy hydrodynamical degrees of freedom to the integrated-out, UV degrees o…
We find an analytical solution to relativistic viscous hydrodynamics for a 1+1 dimensional Landau flow profile. We consider relativistic Navier-Stokes form of the dissipative hydrodynamic equation, for a non-conformal system with a constant speed of sound, and employ the obtained solution to fit rapidity spectrum of observed pions in $\sqrt{s_{NN}}=$ 200, 17.3, 12.3, 8.76, 7.62, 6.27, 4.29, 3.83, 3.28 and 2.63 GeV collision energies. We find that at the freeze-out hypersurface with improved Landau's freeze-out prescription, the viscous corrections do not affect the rapidity spectra. We demonst…
In ref. \cite{1406.7222}, we reported a construction of all order linearized fluid dynamics with strongly coupled $\mathcal{N}=4$ super-Yang-Mills theory as underlying microscopic description. The linearized fluid/gravity correspondence makes it possible to resum all order derivative terms in the fluid stress tensor. Dissipative effects are fully encoded by the shear term and a new one, emerging starting from third order in hydrodynamic derivative expansion. In this work, we provide all computational details omitted in \cite{1406.7222} and present additional results. We derive closed-form line…
We find the general analytical solution of the viscous relativistic hydrodynamic equations (in the absence of bulk viscosity and chemical potential) for a Bjorken expanding fluid with a constant shear viscosity relaxation time. We analytically determine the hydrodynamic attractor of this fluid and discuss its properties. We show for the first time that the slow-roll expansion, a commonly used approach to characterize the attractor, diverges. This is shown to hold also in a conformal plasma. The gradient expansion is found to converge in an example where causality and stability are violated.
We generalize (linearized) relativistic hydrodynamics by including all order gradient expansion of the energy momentum tensor, parametrized by four momenta-dependend transport coefficients, one of which is the usual shear viscosity. We then apply the AdS/CFT duality for ${\cal N}=4$ SUSY in order to compute the retarded correlators of the energy-momentum tensor. From these correlators we determine a large set of transport coefficients of third- and fourth-order hydrodynamics. We find that higher order terms have a tendency to reduce the effect of viscosity.
We consider an isotropic compressible non-dissipative fluid with broken parity subject to free surface boundary conditions in two spatial dimensions. The hydrodynamic equations describing the bulk dynamics of the fluid as well as the free surface boundary conditions depend explicitly on the parity breaking non-dissipative odd viscosity term. We construct a variational principle in the form of an effective action which gives both bulk hydrodynamic equations and free surface boundary conditions. The free surface boundary conditions require an additional boundary term in the action which resemble…
