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Relativistic hydrodynamics for spin-polarized fluids
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Recent progress in the formulation of relativistic hydrodynamics for particles with spin one-half is reviewed. We start with general arguments advising introduction of a tensor spin chemical potential that plays a role of the Lagrange multiplier coupled to the spin angular momentum. Then, we turn to a discussion of spin-dependent distribution functions that have been recently proposed to construct a hydrodynamic framework including spin and serve as a tool in phenomenological studies of hadron polarization. Distribution functions of this type are subsequently used to construct the equilibrium Wigner functions that are employed in the semi-classical kinetic equation. The semi-classical expansion elucidates several aspects of the hydrodynamic approach, in particular, shows the ways in which different possible versions of hydrodynamics with spin can be connected by pseudo-gauge transformations. These results point out at using the de~Groot - van~Leeuwen - van~Weert versions of the energy-momentum and spin tensors as the most natural and complete physical variables. Finally, a totally new method is proposed to design hydrodynamics with spin, which is based on the classical treatment of spin degrees of freedom. Interestingly, for small values of the spin chemical potential the new scheme brings the results that coincide with those obtained before. The classical approach also helps us to resolve problems connected with the normalization of the spin polarization three-vector. In addition, it clarifies the role of the Pauli-Lubanski vector and the entropy current conservation. We close our review with several general comments presenting possible future developments of the discussed frameworks.
Forward citations
Cited by 15 Pith papers
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Local Spin Polarization in Anisotropic Gubser Flow: Suppression Mechanism and Formulation Dependence
In an anisotropic Gubser flow, the longitudinal spin polarization's sign depends on which shear formulation is used, and two popular formulations show exact or near-exact cancellation between vorticity and shear contr...
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A symmetry-based resolution of pseudo-gauge ambiguities in local equilibrium
Local-equilibrium density operators built only from genuine conserved currents are invariant under pseudo-gauge and improvement transformations of the energy-momentum and spin tensors.
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Nonlinear causality and stability of perfect spin hydrodynamics and its nonperturbative character
All four studied formulations of perfect spin hydrodynamics satisfy divergence-type structure and are nonlinearly causal and stable when exact, nonperturbative distribution functions are used.
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Relativistic spin hydrodynamics with antisymmetric spin tensors and an extension of the Bargmann-Michel-Telegdi equation
A new entropy-principle formulation of relativistic spin hydrodynamics yields a modified BMT spin evolution equation and spin-induced transport corrections that map onto inverse and anomalous Hall effects.
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On the local thermodynamic relations in relativistic spin hydrodynamics
For free fermions in rotating and accelerating global equilibrium, the derivative of pressure with respect to the spin potential differs from the spin density, and no entropy-gauge transformation can restore the stand...
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Generalized relativistic second-order spin hydrodynamics from Zubarev's non-equilibrium statistical operator
Second-order spin hydrodynamics is extended with nonlocal memory corrections, adding new acceleration-dependent terms to diffusion, rotational stress, and heat-current equations.
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Spin alignment of vector mesons in local equilibrium by Zubarev's approach
The spin alignment rho00-1/3 vanishes at first order in gradients in local equilibrium, with nonzero contributions first appearing at second order, in a pseudo-gauge dependent way.
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Spin polarization of an expanding and rotating system
Derives closed equations for spin moments and a first-order longitudinal polarization formula for a boost-invariant, rotating relativistic fluid, connecting free streaming to hydrodynamics.
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Spin dynamics with realistic hydrodynamic background for relativistic heavy-ion collisions
Solving perfect spin hydrodynamics on a realistic 3+1D Au+Au background requires the spin evolution to start near 4 fm/c to describe Lambda polarization data.
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Thermodynamics of rotating fermions
A local pressure for rotating massless fermions is proposed that satisfies both the Euler relation and the thermodynamic differential relations, resolving a known spin-hydrodynamics tension.
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Dynamics of Hot QCD Matter 2024 -- Bulk Properties
This proceedings volume collects 19 conference contributions on the bulk properties of hot QCD matter, mostly extending established models and comparing them with lattice QCD and heavy-ion data.
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Quasiparticle second-order dissipative hydrodynamics at finite chemical potential
A quasiparticle kinetic theory with a bag term yields second-order equations of relativistic dissipative hydrodynamics with baryon diffusion and chemical-potential-dependent transport coefficients.
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Local spin polarization of $\Lambda$ hyperons and its interaction corrections
The CLVisc hydrodynamic model reproduces the second sine Fourier coefficient of Lambda longitudinal polarization in Au+Au collisions but fails in p+Pb collisions; the paper also surveys quantum kinetic theory and spin...
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Spin hydrodynamics
The paper proposes a hybrid perfect and dissipative spin hydrodynamics built on generalized tensor thermodynamic relations, but it contains no new derivation beyond the cited prior works.
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An introduction to relativistic spin hydrodynamics
A review that derives the constitutive equations of relativistic spin hydrodynamics from thermodynamics and surveys challenges like pseudo-gauge ambiguity and spin freeze-out.
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