We present a new derivation of relativistic second-order dissipative hydrodynamics for quantum systems using Zubarev's non-equilibrium statistical-operator formalism. This is achieved by a systematic expansion of the energy-momentum tensor and the charge current to second order in deviations from equilibrium. As a concrete example, we obtain the relaxation equations for the shear-stress tensor, the bulk-viscous pressure, and the charge-diffusion currents required to close the set of equations of motion for relativistic second-order dissipative hydrodynamics. We also identify new transport coefficients which describe the relaxation of dissipative processes to second order and express them in terms of equilibrium correlation functions, thus establishing new Kubo-type formulas for second-order transport coefficients.
We use the Crooks fluctuation theorem together with Zubarev hydrodynamics to develop a bottom-up theory of hydrodynamic fluctuations. We also use thermodynamic uncertainity relations to estimate bottom-up limits to dissipative transport coefficients.
We revisit the construction of first-order spin hydrodynamics and find that the constitution relations receive the corrections from the cross effects resulting from spin-orbit coupling. Starting from a routine entropy analysis, we show how to identify cross effects and new cross transport coefficients from the second law of thermodynamics. Interestingly, the conventional transport coefficient heat conductivity $κ$ is bounded from below by the product of cross transport coefficients, which means the threshold of heat conduction is changed. With recourse to Zubarev's non-equilibrium statistical …
Development of a new framework for derivation of order-by-order hydrodynamics from Boltzmann equation is necessary as the widely used Anderson-Witting formalism leads to violation of fundamental conservation laws when the relaxation-time depends on particle energy, or in a hydrodynamic frame other than the Landau frame. We generalize an existing framework for consistent derivation of relativistic dissipative hydrodynamics from the Boltzmann equation with a energy-dependent relaxation-time by extending the Anderson-Witting relaxation-time approximation. We argue that the present framework is co…
In this work, we perform a phenomenological derivation of the first- and second-order relativistic hydrodynamics of dissipative fluids. To set the stage, we start with a review of the ideal relativistic hydrodynamics from energy-momentum and particle number conservation equations. We then go on to discuss the matching conditions to local thermodynamical equilibrium, symmetries of the energy-momentum tensor, decomposition of dissipative processes according to their Lorentz structure, and finally, the definition of the fluid velocity in the Landau and Eckart frames. With this preparatory work, w…
We derive relativistic second-order dissipative fluid-dynamical equations of motion for massive spin-1/2 particles from kinetic theory using the method of moments. Besides the usual conservation laws for charge, energy, and momentum, such a theory of relativistic dissipative spin hydrodynamics features an equation of motion for the rank-3 spin tensor, which follows from the conservation of total angular momentum. Extending the conventional method of moments for spin-0 particles, we expand the spin-dependent distribution function near local equilibrium in terms of moments of the momentum and sp…
We argue that different formulations of hydrodynamics are related to uncertainties in the definitions of local thermodynamic and hydrodynamic variables. We show that this ambiguity can be resolved by viewing different formulations of hydrodynamics as particular "gauge choices" which lead to the same physical behavior of the system. Using the example of bulk viscosity, we show that Bemfica-Disconzi-Noronha-Kovtun (BDNK) and Israel-Stewart hydrodynamics are particular "gauge choices" of this type, related by a well-defined transformation of thermodynamic and hydrodynamic variables. We argue that…
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…
We derive a set of nontrivial relations between second-order transport coefficients which follow from the second law of thermodynamics upon considering a regime close to uniform rotation of the fluid. We demonstrate that extension of hydrodynamics by spin variable is equivalent to modifying conventional hydrodynamics by a set of second-order terms satisfying the relations we derived. We point out that a novel contribution to the heat current orthogonal to vorticity and temperature gradient reminiscent of the thermal Hall effect is constrained by the second law.
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.
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…
