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Relativistic second-order spin hydrodynamics: an entropy-current analysis
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abstract
We present a new derivation of Israel-Stewart-like relativistic second-order dissipative spin hydrodynamic equations using the entropy current approach. In our analysis, we consider a general energy-momentum tensor with symmetric and anti-symmetric parts. Moreover, the spin tensor, which is not separately conserved, has a simple phenomenological form that is antisymmetric only in the last two indices. Apart from the evolution equations for energy density, fluid flow, and spin density, we also find relaxation-type dynamical equations for various dissipative currents. The latter are consistently derived within the second-order theory as gradient corrections to the energy-momentum and spin tensors. We argue that this approach correctly reproduces the corresponding Navier-Stokes limit of spin hydrodynamic equations. Throughout our analysis, the spin chemical potential is considered a $\mathcal{O}(\partial)$ quantity in the hydrodynamic gradient expansion and reduces to thermal vorticity in the global equilibrium. New coefficients appearing in the generalized spin hydrodynamic equations are undetermined and can only be evaluated within a proper underlying microscopic theory of a given system.
Forward citations
Cited by 7 Pith papers
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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 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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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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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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