We introduce a new framework of highly-anisotropic hydrodynamics that includes dissipation effects. Dissipation is defined by the form of the entropy source that depends on the pressure anisotropy and vanishes for the isotropic fluid. With a simple ansatz for the entropy source obeying general physical requirements, we are led to a non-linear equation describing the time evolution of the anisotropy in purely-longitudinal boost-invariant systems. Matter that is initially highly anisotropic approaches naturally the regime of the perfect fluid. Thus, the resulting evolution agrees with the expectations about the behavior of matter produced at the early stages of relativistic heavy-ion collisions. The equilibration is identified with the processes of entropy production.
We argue that there is correspondence between the perfect nonextensive hydrodynamics and the usual dissipative hydrodynamics, which we call nonextensive/dissipative correspondence (NexDC). It leads to simple expression for dissipative entropy current and allows for predictions for the ratio of bulk and shear viscosities to entropy density, $ζ/s$ and $η/s$.
We argue that there is profound correspondence (the nonextensive/dissipative correspondence - NexDC) between the perfect nonextensive hydrodynamics and the usual dissipative hydrodynamics which leads to simple expression for dissipative entropy current.
We demonstrate that nonextensive perfect relativistic hydrodynamics ($q$-hydrodynamics) can serve as a model of the usual relativistic dissipative hydrodynamics ($d$-hydrodynamics) facilitating therefore considerably its applications. As 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 $η/s$.
We propose to model the dissipative hydrodynamics used in description of the multiparticle production processes ($d$-hydrodynamics) by a special kind of the perfect nonextensive fluid ($q$-fluid) where $q$ denotes the nonextensivity parameter appearing in the nonextensive Tsallis statistics. The advantage of $q$-hydrodynamics lies in its formal simplicity in comparison to the $d$-hydrodynamics. We argue that parameter $q$ describes summarily (at least to some extent) all dynamical effects behind the viscous behavior of the hadronic fluid.
We derive the constitutive equations of causal relativistic dissipative hydrodynamics ($d$-hydrodynamics) from perfect nonextensive hydrodynamics ($q$-hydrodynamics) using the nonextensive/dissipative correspondence (NexDC) proposed by us recently. The $q$-hydrodynamics can be thus regarded as a possible model for the $d$-hydrodynamics facilitating its application to high energy multiparticle production processes. As an example we have shown that applying the NexDC to the perfect 1+1 $q$-hydrodynamics, one obtains a proper time evolution of the bulk pressure and the Reynolds number.
Kinetic and hydrodynamic models describing early stages of relativistic heavy-ion collisions are discussed. We emphasise the role of the shear-bulk coupling for the correct determination of the time dependence of the bulk viscous pressure.
High-energy heavy ion collider experiments at RHIC and LHC have revealed that relativistic hydrodynamic models describe the hot and dense quark matter quantitatively. In this study, I develop a novel dissipative hydrodynamic model at finite baryon density to investigate the net baryon rapidity distribution. The results show that the distribution is widened in hydrodynamic evolution, which implies that the transparency of the collisions is effectively enhanced. This suggests that the kinetic energy loss for medium production at the initial stage could be larger. Furthermore, the net baryon dist…
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.
The stability and causality of the Landau-Lifshitz theory and the Israel-Stewart type causal dissipative hydrodynamics are discussed. We show that the problem 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.
The recently formulated framework of anisotropic and dissipative hydrodynamics (ADHYDRO) is used to describe non-boost-invariant motion of the fluid created at the early stages of heavy-ion collisions. Very strong initial asymmetries of pressure are reduced by the entropy production processes. By the appropriate choice of the form of the entropy source we can reproduce realistic scenarios for the isotropization expected in heavy-ion collisions. Our previous results are generalized by including the realistic equation of state as the limit of the isotropization processes.
We have derived the analytic solutions of dissipative relativistic spin hydrodynamics with Gubser expansion. Following the standard strategy of deriving the solutions in a Gubser flow, we take the Weyl rescaling and obtain the energy-momentum and angular momentum conversation equations in the $dS_{3}\times\mathbb{R}$ space-time. We then derive the analytic solutions of spin density, spin potential and other thermodynamic in $dS_{3}\times\mathbb{R}$ space-time and transform them back into Minkowski space-time $\mathbb{R}^{3,1}$. In the Minkowski space-time, the spin density and spin potential i…
We derive the multi-component second-order dissipative relativistic hydrodynamic equations using the moment-expansion method. By computing the transport coefficients using hard-sphere interactions, we investigate the role of multiple components and the reactive collisions. We find that both of these factors increase the effective cross-section and hence decrease the transport coefficients and relaxation times. We further compute such transport properties using leading-order perturbative QCD cross-sections. For both types of cross-sections, we find that the ratio between vector current relaxati…
A recently obtained set of the equations for leading-order (3+1)D anisotropic hydrodynamics is tested against exact solutions of the Boltzmann equation with the collisional kernel treated in the relaxation time approximation. In order to perform the detailed comparisons, the new anisotropic hydrodynamics equations are reduced to the boost-invariant and transversally homogeneous case. The agreement with the exact solutions found using the new anisotropic hydrodynamics equations is similar to that found using previous, less general, formulations of anisotropic hydrodynamics. In addition, we find…
Relativistic dissipative hydrodynamic equations are extended by taking into account particle number changing processes in a gluon system, which expands in one dimension boost-invariantly. Chemical equilibration is treated by a rate equation for the particle number density based on Boltzmann equation and Grad's ansatz for the off-equilibrium particle phase space distribution. We find that not only the particle production, but also the temperature and the momentum spectra of the gluon system, obtained from the hydrodynamic calculations, are sensitive to the rates of particle number changing proc…
The quark gluon plasma generated in ultrarelativistic heavy ion collisions may possess sizable momentum-space anisotropies that cause the longitudinal and transverse pressures in the local rest frame to be significantly different. We review recent attempts to derive a dynamical framework that can reliably describe systems that possess a high degree of momentum-space anisotropy. The dynamical framework that has been developed can describe the evolution of the quark gluon plasma ranging from the longitudinal free-streaming limit to the ideal hydrodynamical limit.
We exactly solve the relaxation-time approximation Boltzmann equation for a system which is transversely homogeneous and undergoing boost-invariant longitudinal expansion. We compare the resulting exact numerical solution with approximate solutions available in the anisotropic hydrodynamics and second order viscous hydrodynamics frameworks. In all cases studied, we find that the anisotropic hydrodynamics framework is a better approximation to the exact solution than traditional viscous hydrodynamical approaches.
We compute the gradient expansion for anisotropic hydrodynamics. The results are compared with the corresponding expansion of the underlying kinetic-theory model with the collision term treated in the relaxation time approximation. We find that a recent formulation of anisotropic hydrodynamics based on an anisotropic matching principle yields the first three terms of the gradient expansion in agreement with those obtained for the kinetic theory. This gives further support for this particular hydrodynamic model as a good approximation of the kinetic-theory approach. We further find that the gra…
In this contribution we study the effects of three transport coefficients of dissipative hydrodynamics on thermal dilepton anisotropic flow observables. The first two transport coefficients investigated influence the overall size and growth rate of shear viscous pressure, while the last transport coefficient governs the magnitude of net baryon number diffusion in relativistic dissipative fluid dynamics. All calculations are done using state-of-the-art 3+1D hydrodynamical simulations. We show that thermal dileptons are sensitive probes of the transport coefficients of dissipative hydrodynamics.
We studied the shock propagation and its stability with the causal dissipative hydrodynamics in 1+1 dimensional systems. We show that the presence of the usual viscosity is not enough to stabilize the solution. This problem is solved by introducing an additional viscosity which is related to the coarse-graining scale of the theory.
In this paper we present a method to improve the description of 0+1 dimensional boost invariant dissipative dynamics in the presence of large momentum-space anisotropies. We do this by reorganizing the canonical hydrodynamic expansion of the distribution function around a momentum-space anisotropic ansatz rather than an isotropic equilibrium one. At leading order the result obtained is two coupled ordinary differential equations for the momentum-space anisotropy and typical momentum of the degrees of freedom. We show that this framework can reproduce both the ideal hydrodynamic and free stream…
The one-dimensional non-boost-invariant evolution of the quark-gluon plasma, presumably produced during the early stages of heavy-ion collisions, is analyzed within the frameworks of viscous and anisotropic hydrodynamics. We neglect transverse dynamics and assume homogeneous conditions in the transverse plane but, differently from Bjorken expansion, we relax longitudinal boost invariance in order to study the rapidity dependence of various hydrodynamical observables. We compare the results obtained using several formulations of second-order viscous hydrodynamics with a recent approach to aniso…
We apply divergence-type theory (DTT) dissipative hydrodynamics to study the 2+1 space-time evolution of the fireball created in Au+Au relativistic heavy-ion collisions at $\sqrt{s_{NN}}=$200 GeV. DTTs are exact hydrodynamic theories that do no rely on velocity gradient expansions and therefore go beyond second-order theories. We numerically solve the equations of motion of the DTT for Glauber initial conditions and compare the results with those of second-order theory based on conformal invariants (BRSS) and with data. We find that the charged-hadron minumum-bias elliptic flow reaches its max…
We exactly solve the one-dimensional boost-invariant Boltzmann equation in the relaxation time approximation for arbitrary shear viscosity. The results are compared with the predictions of viscous and anisotropic hydrodynamics. Studying different non-equilibrium cases and comparing the exact kinetic-theory results to the second-order viscous hydrodynamics results we find that recent formulations of second-order viscous hydrodynamics agree better with the exact solution than the standard Israel-Stewart approach. Additionally, we find that, given the appropriate connection between the kinetic an…
We review the entropy based derivation of third-order hydrodynamic equations and compare their solutions in one-dimensional boost-invariant geometry with calculations by the partonic cascade BAMPS. We demonstrate that Grad's approximation, which underlies the derivation of both Israel-Stewart and third-order equations, describes the transverse spectra from BAMPS with high accuracy. At the same time solutions of third-order equations are much closer to BAMPS results than solutions of Israel-Stewart equations. Introducing a resummation scheme for all higher-oder corrections to one-dimensional hy…
We propose a stable first-order relativistic dissipative hydrodynamic equation in the particle frame (Eckart frame) for the first time. The equation to be proposed was in fact previously derived by the authors and a collaborator from the relativistic Boltzmann equation. We demonstrate that the equilibrium state is stable with respect to the time evolution described by our hydrodynamic equation in the particle frame. Our equation may be a proper starting point for constructing second-order causal relativistic hydrodynamics, to replace Eckart's particle-flow theory.
In this proceedings, we review the basics of quasiparticle anisotropic hydrodynamics (aHydroQP). Thenwe present phenomenological comparisons between 3+1d quasiparticle anisotropic hydrodynamics and experimental data from RHIC experiments at 200 GeV Au-Au collisions. We show that 3+1d aHydroQP model is able to describe the experimental results quite well for the spectra, multiplicity, and elliptic flow for charged particles in different centrality classes.
In this proceedings contribution, we will review the basics of quasiparticle anisotropic hydrodynamics. Then, we will present some recent phenomenological results of 3+1d quasiparticle anisotropic hydrodynamics and Pb-Pb $2.76$ TeV collisions from the ALICE collaboration. We show that 3+1d quasiparticle anisotropic hydrodynamics model is able to describe the experimental results for Pb-Pb collisions at $2.76$ TeV quite well for many observables such as the spectra, the elliptic flow, and HBT radii in many centrality classes.
We study an azimuthally-symmetric boost-invariant quark-gluon plasma using quasiparticle anisotropic hydrodynamics including the effects of both shear and bulk viscosities. We compare results obtained using the quasiparticle method with the standard anisotropic hydrodynamics and viscous hydrodynamics. We consider the predictions of the three methods for the differential particle spectra and mean transverse momentum. We find that the three methods agree for small shear viscosity to entropy density ratio, $η/s$, but show differences at large $η/s$. Additionally, we find that the standard anisotr…
The quark-gluon plasma is considered to behave as a relativistic viscous fluid in the high-energy heavy ion collisions. In this study, I develop and estimate a second order dissipative hydrodynamic model at finite baryon density with effects of baryon dissipation together with those of shear and bulk viscosities. It is found that the hydrodynamic evolution effectively reduces baryon stopping, suggesting that the collisions are less transparent at the initial stage. Also the net baryon distribution is found sensitive to baryon dissipation as well as to viscosities. The results indicate that the…
Anisotropic-hydrodynamics framework is used to describe a mixture of quark and gluon fluids. The effects of quantum statistics, finite quark mass, and finite baryon number density are taken into account. The results of anisotropic hydrodynamics are compared with exact solutions of the coupled kinetic equations for quarks and gluons in the relaxation time approximation. The overall very good agreement between the hydrodynamic and kinetic-theory results is found.
The framework of leading-order anisotropic hydrodynamics is supplemented with realistic equation of state and self-consistent freeze-out prescription. The model is applied to central proton-nucleus collisions. The results are compared to those obtained within standard Israel-Stewart second-order viscous hydrodynamics. It is shown that the resulting hadron spectra are highly-sensitive to the hydrodynamic approach that has been used.
Using second--order dissipative hydrodynamics coupled self-consistently to the linear $σ$ model we study the 2+1 dimensional evolution of the fireball created in Au+Au relativistic collisions. We analyze the influence of the dynamics of the chiral fields on the charged-hadron elliptic flow $v_2$ and on the ratio $v_4/(v_2)^2$ for a temperature-independent as well as for a temperature-dependent viscosity-to-entropy ratio $η/s$ calculated from the linearized Boltzmann equation in the relaxation time approximation. We find that $v_2$ is not very sensitive to the coupling of chiral sources to the …
In this paper we review recent progress in relativistic anisotropic hydrodynamics. We begin with a pedagogical introduction to the topic which takes into account the advances in our understanding of this topic since its inception. We consider both conformal and non-conformal systems and demonstrate how one can implement a realistic equation of state using a quasiparticle approach. We then consider the inclusion of non-spheroidal (non-ellipsoidal) corrections to leading-order anisotropic hydrodynamics and present the findings of the resulting second-order viscous anisotropic hydrodynamics frame…
We have studied analytically the longitudinally boost-invariant motion of a relativistic dissipative fluid with spin. We have derived the analytic solutions of spin density and spin chemical potential as a function of proper time $τ$ in the presence of viscous tensor and the second order relaxation time corrections for spin. Interestingly, analogous to the ordinary particle number density and chemical potential, we find that the spin density and spin chemical potential decay as $\simτ^{-1}$ and $\simτ^{-1/3}$, respectively. It implies that the initial spin density may not survive at the freeze…
We use the entropy production variational method to associate a one particle distribution function to the assumed known energy-momentum and entropy currents describing a relativistic conformal fluid. Assuming a simple form for the collision operator we find this one particle distribution function explicitly, and show that this method of linking the hydro and kinetic description is a non trivial generalization of Grad's ansatz. The resulting constitutive relations are the same as in the conformal dissipative type theories discussed in J. Peralta-Ramos and E. Calzetta, Phys. Rev. D {\bfseries 80…
We present a new derivation of relativistic dissipative hydrodynamic equations, which invokes the second law of thermodynamics for the entropy four-current expressed in terms of the single-particle phase-space distribution function obtained from Grad's 14-moment approximation. This derivation is complete in the sense that all the second-order transport coefficients are uniquely determined within a single theoretical framework. In particular, this removes the long-standing ambiguity in the relaxation time for bulk viscosity thereby eliminating one of the uncertainties in the extraction of the s…
We discuss the leading order of anisotropic hydrodynamics expansion. It has already been shown that in the (0+1) and (1+1)-dimensional cases it is consistent with the second order viscous hydrodynamics, and it provides a striking agreement with the exact solutions of the Boltzmann equation. Quite recently, a new set of equations has been proposed for the leading order of anisotropic hydrodynamics, which is consistent with the second order viscous hydrodynamics in the most general (3+1)-dimensional case, and does not require a next-to-leading treatment for describing pressure anisotropies in th…
Second-order dissipative hydrodynamic equations for each component of a multi-component system are derived using the entropy principle. The shear viscosity of the whole system, appearing in the equation summed-up over all components, is related to the partial shear pressures and cannot be considered as an external parameter. We demonstrate that it is essential to solve hydrodynamic equations for each component, instead of treating a mixture as an effective one-component system with a free parameter $η/s$. Thus, extractions of the $η/s$ value of the QGP at RHIC and LHC have to be reexamined.
We present a new formalism for the theory of relativistic dissipative hydrodynamics. Here, we look for the minimal structure of such a theory which satisfies the covariance and causality 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). It can readily be applied to the full three-dimensional hydrodynamical calculations. We apply our formalism to the Bjorken model and the results are shown to be analogous to the IS.
Anisotropic hydrodynamics improves upon standard dissipative fluid dynamics by treating certain large dissipative corrections non-perturbatively. Relativistic heavy-ion collisions feature two such large dissipative effects: (i) Strongly anisotropic expansion generates a large shear stress component which manifests itself in very different longitudinal and transverse pressures, especially at early times. (ii) Critical fluctuations near the quark-hadron phase transition lead to a large bulk viscous pressure on the conversion surface between hydrodynamics and a microscopic hadronic cascade descri…
In this proceedings contribution I review recent progress in our understanding of the bulk dynamics of relativistic systems that possess potentially large local rest frame momentum-space anisotropies. In order to deal with these momentum-space anisotropies, a reorganization of relativistic viscous hydrodynamics can been made around an anisotropic background, and the resulting dynamical framework has been dubbed "anisotropic hydrodynamics." I also discuss expectations for the degree of momentum-space anisotropy of the quark gluon plasma generated in relativistic heavy ion collisions at RHIC and…
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.
We use quasiparticle anisotropic hydrodynamics to study an azimuthally-symmetric boost-invariant quark-gluon plasma including the effects of both shear and bulk viscosities. In quasiparticle anisotropic hydrodynamics, a single finite-temperature quasiparticle mass is introduced and fit to the lattice data in order to implement a realistic equation of state. We compare results obtained using the quasiparticle method with the standard method of imposing the equation of state in anisotropic hydrodynamics and viscous hydrodynamics. Using these three methods, we extract the primordial particle spec…
Starting from the Boltzmann equation in the relaxation time approximation and employing a Chapman-Enskog like expansion for the distribution function close to equilibrium, we derive second-order evolution equations for the shear stress tensor and the dissipative charge current for a system of massless quarks and gluons. The transport coefficients are obtained exactly using quantum statistics for the phase space distribution functions at non-zero chemical potential. We show that, within the relaxation time approximation, the second-order evolution equations for the shear stress tensor and the d…
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. {\bf C 85}, (2012) 14906]. We extend this formalism further to the arbitrary Lorentz frame. We discuss the stability and causality of solutions of fluid equations which are obtained by applying this formulation to the Landau 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 po…
In this proceedings contribution, we review 3+1d quasiparticle anisotropic hydrodynamics (aHydroQP). Then, we show some recent phenomenological comparisons between the aHydroQP model and some experimental results. We show comparisons between aHydroQP and Pb-Pb 2.76 TeV collisions from the ALICE collaboration and Au-Au 200 GeV collisions from RHIC experiments. We show that the quasiparticle anisotropic hydrodynamics model is able to describe the experimental results for Pb-Pb and Au-Au collisions quite well for many observables such as the spectra, multiplicity, elliptic flow, and HBT radii in …
We use leading-order anisotropic hydrodynamics to study an azimuthally-symmetric boost-invariant quark-gluon plasma. We impose a realistic lattice-based equation of state and perform self-consistent anisotropic freeze-out to hadronic degrees of freedom. We then compare our results for the full spatiotemporal evolution of the quark-gluon plasma and its subsequent freeze-out to results obtained using 1+1d Israel-Stewart second-order viscous hydrodynamics. We find that for small shear viscosities, 4 pi eta/s ~ 1, the two methods agree well for nucleus-nucleus collisions, however, for large shear …
We compute dilepton production from the deconfined phase of the quark-gluon plasma using leading-order (3+1)-dimensional anisotropic hydrodynamics. The anisotropic hydrodynamics equa- tions employed describe the full spatiotemporal evolution of the transverse temperature, spheroidal momentum-space anisotropy parameter, and the associated three-dimensional collective flow of the matter. The momentum-space anisotropy is also taken into account in the computation of the dilepton production rate, allowing for a self-consistent description of dilepton production from the quark-gluon plasma. For our…
In this review, we present the motivation for using relativistic anisotropic hydrodynamics to study the physics of ultrarelativistic heavy-ion collisions. We then highlight the main ingredients of the 3+1D quasiparticle anisotropic hydrodynamics model and present phenomenological comparisons with experimental data at different collision energies. These comparisons show that anisotropic hydrodynamics can describe many bulk observables of the quark-gluon plasma.
The recently formulated framework of anisotropic hydrodynamics is used in 3+1 dimensions to study behavior of matter created in relativistic heavy-ion collisions. The model predictions for various hadronic observables show that the effects of the initial anisotropy of pressure may be compensated by appropriate adjustment of the initial energy density. In this way, the final hadronic observables become insensitive to the early stage dynamics and the early thermalization/isotropization puzzle may be circumvented.
A significant fraction of the changes in momentum distributions induced by dissipative phenomena in the description of the fluid fireball created in ultrarelativistic heavy-ion collisions actually take place when the fluid turns into individual particles. We study these corrections in the limit of a low freeze-out temperature of the flowing medium, and we show that they mostly affect particles with a higher velocity than the fluid. For these, we derive relations between different flow harmonics, from which the functional form of the dissipative corrections could ultimately be reconstructed fro…
We briefly discuss the recent developments in causal dissipative hydrodynamic for relativistic heavy ion collisions. Phenomenological estimate of QGP viscosity over entropy ratio from several experimental data, e.g. STAR's $ϕ$ meson data, centrality dependence of elliptic flow, universal scaling elliptic flow etc. are discussed. QGP viscosity, extracted from hydrodynamical model analysis can have very large systematic uncertainty due to uncertain initial conditions.
Tensors describing boost-invariant and cylindrically symmetric expansion of a relativistic dissipative fluid are decomposed in a suitable chosen basis of projection operators. This leads to a simple set of scalar equations which determine the fluid behavior. As special examples, we discuss the case of the Israel-Stewart theory and the model of highly-anisotropic and strongly-dissipative hydrodynamics ADHYDRO. We also introduce the matching conditions between the ADHYDRO description suitable for the very early stages of heavy-ion collisions and the Israel-Stewart theory applicable for later sta…
We report part of our recent work on viscous hydrodynamics with consistent phase space distribution $f(x,\p)$ for freeze out. We develop the gradient expansion formalism based on kinetic theory, and with the constraints from the comparison between hydrodynamics and kinetic theory, viscous corrections to $f(x,\p)$ can be consistently determined order by order. Then with the obtained $f(x,\p)$, second order viscous hydrodynamical calculations are carried out for elliptic flow $v_2$.
