Relativistic Dissipative Hydrodynamics Research Articles

Anisotropic hydrodynamics and early stages of heavy-ion collisions

New formulations of relativistic dissipative hydrodynamics are discussed in the context of possible applications to describe early stages of relativistic heavy-ion collisions. The efficacy of different approaches is tested by making comparisons with the exact solutions of the kinetic equation.

Towards an effective action for relativistic dissipative hydrodynamics

We propose an effective action for first order relativistic dissipative hydrodynamics that can be used to evaluate n-point symmetrized correlation functions, taking into account thermal fluctuations of the hydrodynamic variables.

Relativistic dissipative hydrodynamics from kinetic theory with relaxation-time approximation

Starting from Boltzmann equation with relaxation time approximation for the collision term and using Chapman-Enskog like expansion for distribution function close to equilibrium, we derive hydrodynamic evolution equations for the dissipative quantities directly from their definition. Although the form of the equations is identical to those obtained in traditional Israel-Stewart approaches employing Grad's 14-moment approximation and second moment of Boltzmann equation, the coefficients obtained are different. In the case of one-dimensional scaling expansion, we demonstrate that our results are in better agreement with numerical solution of Boltzmann equation as compared to Israel-Stewart results. We also show that including approximate higher-order corrections in viscous evolution significantly improves this agreement, thus justifying the relaxation time approximation for the collision term.

Relativistic dissipative hydrodynamics with extended matching conditions for ultra-relativistic heavy-ion collisions

Recently we proposed a novel approach to the formulation of relativistic dissipative hydrodynamics by extending the so-called matching conditions in the Eckart frame (Phys. Rev. C 85, 14906 (2012)). We extend this formalism further to the arbitrary local rest frame. We discuss the stability and causality of solutions of fluid equations which are obtained by applying this formulation to the Landau-Lifshitz frame, which is more relevant to treat the fluid produced in ultra-relativistic heavy-ion collisions. We derive equations of motion for a relativistic dissipative fluid with zero baryon chemical potential and show that linearized equations obtained from them are stable against small perturbations. It is found that conditions for a fluid to be stable against infinitesimal perturbations are equivalent to imposing restrictions that the sound wave, $c_{s}$ , propagating in the fluid, must not exceed the speed of light c, i.e., $c_{s} < c$ . This conclusion is equivalent to that obtained in the previous paper using the Eckart frame (Phys. Rev. C 85, 14906 (2012)).

On the inertia of heat

Does heat have inertia? This question is at the core of a long-standing controversy on Eckart's dissipative relativistic hydrodynamics. Here I show that the troublesome inertial term in Eckart's heat flux arises only if one insists on defining thermal diffusivity as a spacetime constant. I argue that this is the most natural definition, and that all confusion disappears if one considers instead the space-dependent comoving diffusivity, in line with the fact that, in the presence of gravity, space is an inhomogeneous medium.

First order and stable relativistic dissipative hydrodynamics

Relativistic thermodynamics is derived from kinetic equilibrium in a general frame. Based on a novel interpretation of Lagrange multipliers in the equilibrium state we obtain a generic stable but first order relativistic dissipative hydrodynamics. Although this was believed to be impossible, we circumvent this difficulty by a specific handling of the heat flow.

Modification of Eckart theory of relativistic dissipative fluid dynamics by introducing extended matching conditions

We deal with a novel approach to formulation of the relativistic dissipative hydrodynamics by extending the so-called matching conditions widely used in the literature. The form of the non-equilibrium entropy current can be determined by requiring thermodynamical stability of the entropy current under extended matching conditions. We derive equations of motion for the relativistic dissipative fluid based on the Eckart theory and show that linearized equations obtained from them are stable against small perturbations. It is also shown that the required fluid stability conditions are related to the causality of the model.

Can transport peak explain the low-mass enhancement of dileptons at RHIC?

We propose a novel relation between the low-mass enhancement of dielectrons observed at PHENIX and transport coefficients of QGP such as the charge diffusion constant D and the relaxation time τJ. We parameterize the transport peak in the spectral function using the second-order relativistic dissipative hydrodynamics by Israel and Stewart. Combining the spectral function and the full (3+1)-dimensional hydrodynamical evolution with the lattice EoS, theoretical dielectron spectra and the experimental data are compared. Detailed analysis suggests that the low-mass dilepton enhancement originates mainly from the high-temperature QGP phase where there is a large electric charge fluctuation as obtained from lattice QCD simulations.

A fast numerical scheme for causal relativistic hydrodynamics with dissipation

In this paper, we develop a stable and fast numerical scheme for relativistic dissipative hydrodynamics based on Israel–Stewart theory. Israel–Stewart theory is a stable and causal description of dissipation in relativistic hydrodynamics although it includes relaxation process with the timescale for collision of constituent particles, which introduces stiff equations and makes practical numerical calculation difficult. In our new scheme, we use Strang’s splitting method, and use the piecewise exact solutions for solving the extremely short timescale problem. In addition, since we split the calculations into inviscid step and dissipative step, Riemann solver can be used for obtaining numerical flux for the inviscid step. The use of Riemann solver enables us to capture shocks very accurately. Simple numerical examples are shown. The present scheme can be applied to various high energy phenomena of astrophysics and nuclear physics.

Relativistic Dissipative Hydrodynamics with Conserved Currents and Onsager Reciprocal Relations

Relativistic Dissipative Hydrodynamics with Conserved Currents and Onsager Reciprocal Relations

Relativistic Viscous Hydrodynamics for Multi-Component Systems with Multiple Conserved Currents

We would like to formulate relativistic dissipative hydrodynamics for multi-component systems with multiple conserved currents. This is important for analyses of the hot matter created in relativistic heavy ion collisions because particle creations and annihilations of various particle species are frequently taking place there. We show that consistent formulation in such systems involves many non-trivialities, and derive constitutive equations that satisfy Onsager reciprocal relations and describe the systems without ambiguity.

Transport coefficients of causal dissipative relativistic hydrodynamics in lattice gauge simulations

Transport coefficients of causal dissipative relativistic hydrodynamics in lattice gauge simulations

Extension of relativistic dissipative hydrodynamics to third order

Following the procedure introduced by Israel and Stewart, we expand the entropy current up to the third order in the shear stress tensor ${\ensuremath{\pi}}^{\ensuremath{\alpha}\ensuremath{\beta}}$ and derive a novel third-order evolution equation for ${\ensuremath{\pi}}^{\ensuremath{\alpha}\ensuremath{\beta}}$. This equation is solved for the one-dimensional Bjorken boost-invariant expansion. The scaling solutions for various values of the shear viscosity to the entropy density ratio $\ensuremath{\eta}/s$ are shown to be in very good agreement with those obtained from kinetic transport calculations. For the pressure isotropy starting with 1 at ${\ensuremath{\tau}}_{0}=0.4$ fm/$c$, the third-order corrections to Israel-Stewart theory are approximately $10%$ for $\ensuremath{\eta}/s=0.2$ and more than a factor of 2 for $\ensuremath{\eta}/s=3$. We also estimate all higher-order corrections to Israel-Stewart theory and demonstrate their importance in describing highly viscous matters.

Nonextensive perfect hydrodynamics — a model of dissipative relativistic hydrodynamics?

Abstract We demonstrate that nonextensive perfect relativistic hydrodynamics (q-hydrodynamics) can serve as a model of the usual relativistic dissipative hydrodynamics (d-hydrodynamics) therefore facilitating considerably its applications. As an illustration, we show how using q-hydrodynamics one gets the q-dependent expressions for the dissipative entropy current and the corresponding ratios of the bulk and shear viscosities to entropy density, ζ/s and η/srespectively.

Damping of sound waves in superfluid nucleon-hyperon matter of neutron stars

We consider sound waves in superfluid nucleon-hyperon matter of massive neutron-star cores. We calculate and analyze the speeds of sound modes and their damping times due to the shear viscosity and nonequilibrium weak processes of particle transformations. For that, we employ the dissipative relativistic hydrodynamics of a superfluid nucleon-hyperon mixture, formulated recently [1]. We demonstrate that the damping times of sound modes calculated using this hydrodynamics and the ordinary (nonsuperfluid) one, can differ from each other by several orders of magnitude.

On the nature of the so-called generic instabilities in dissipative relativistic hydrodynamics

It is shown that the so-called generic instabilities that appear in the framework of relativistic linear irreversible thermodynamics, describing the fluctuations of a simple fluid close to equilibrium, arise due to the coupling of heat with hydrodynamic acceleration which appears in Eckart's formalism of relativistic irreversible thermodynamics. Further, we emphasize that such behavior should be interpreted as a contradiction to the postulates of linear irreversible thermodynamics (LIT), namely a violation of Onsager's hypothesis on the regression of fluctuations, and not as fluid instabilities. Such contradictions can be avoided within a relativistic linear framework if a Meixner-like approach to the phenomenological equations is employed.

Transport coefficients of non-Newtonian fluid and causal dissipative hydrodynamics

A formula to calculate the transport coefficients of the causal dissipative hydrodynamics is derived by using the projection operator method (Mori-Zwanzig formalism) [T. Koide, Phys. Rev. E 75, 060103(R) (2007)]. This is an extension of the Green-Kubo-Nakano (GKN) formula to the case of non-Newtonian fluids, which is the essential factor to preserve the relativistic causality in relativistic dissipative hydrodynamics. This formula is the generalization of the GKN formula in the sense that it can reproduce the GKN formula in a certain limit. In this work, we extend the previous work so as to apply to more general situations.

Stability and causality in relativistic dissipative hydrodynamics

The stability and causality of the Landau–Lifshitz theory and the Israel–Stewart-type causal dissipative hydrodynamics are discussed. We show that the problems of acausality and instability are correlated in relativistic dissipative hydrodynamics and instability is induced by acausality. We further discuss the stability of the scaling solution. The scaling solution of the causal dissipative hydrodynamics can be unstable against inhomogeneous perturbations.

Relativistic hydrodynamics – causality and stability

Causality and stability in relativistic dissipative hydrodynamics are important conceptual issues. We argue that causality is not restricted to hyperbolic set of differential equations. E.g. heat conduction equation can be causal considering the physical validity of the theory. Furthermore we propose a new concept of relativistic internal energy that clearly separates the dissipative and non-dissipative effects. We prove that with this choice we remove all known instabilities of the linear response approximation of viscous and heat conducting relativistic fluids. In this paper the Eckart choice of the velocity field is applied.

Causal theory of relativistic dissipative hydrodynamics

We present a new formalism for the theory of relativistic dissipative hydrodynamics, where covariance and causality are satisfied by introducing the memory effect in irreversible currents. Our theory has a much simpler structure and thus has several advantages for practical purposes compared to the Israel-Stewart theory (IS). We apply our formalism to the Bjorken model and the results are shown to be analogous to the IS.