Second-order spin hydrodynamics from Zubarev's nonequilibrium statistical operator formalism

Abstract

Using the Zubarev's nonequilibrium statistical operator formalism, we derive the second-order expression for the dissipative tensors in relativistic spin hydrodynamics, {\em viz.} rotational stress tensor (${\tau }_{\mu \nu }$), boost heat vector ($q_{\mu }$), shear stress tensor (${\pi }_{\mu \nu }$), and bulk viscous pressure ($\Pi$). The first two (${\tau }_{\mu \nu }$ and $q_{\mu }$) emerge due to the inclusion of the antisymmetric part in the energy-momentum tensor, which, in turn, governs the conservation of spin angular momentum (${\Sigma }^{\alpha \mu \nu }$). As a result, new thermodynamic forces, generated due to the antisymmetric part of $T_{\mu \nu }$, contain the spin chemical potential. In this work, we have also taken the spin density ($S^{\mu \nu }$) as an independent thermodynamic variable, in addition to the energy density and particle density, thereby resulting in two novel transport coefficients given by the correlation between spin density tensor and rotational stress tensor and vice versa. Additionally, the newly found terms in ${\pi }_{\mu \nu }$ and $\Pi$ are the artifacts of the new thermodynamic forces that arise due to the antisymmetric part of $T^{\mu \nu }$. Finally, we have derived the evolution equations for the aforesaid tensors: ${\tau }_{\mu \nu }$, $q_{\mu }$, ${\pi }_{\mu \nu }$, and $\Pi$.

31 pages

References in corpus (50)

• Global $\Lambda$ hyperon polarization in nuclear collisions: evidence for the most vortical fluid
• Global polarization of $\Lambda$ hyperons in Au+Au collisions at $\sqrt{s_{{}_{NN}}}$ = 200 GeV
• Towards hydrodynamics without an entropy current
• Relativistic fluid dynamics with spin
• Study of Lambda polarization in relativistic nuclear collisions at sqrt{s}_NN = 7.7-200 GeV
• Polarization of $\Lambda$ ($\bar{\Lambda }$) hyperons along the beam direction in Au+Au collisions at $\sqrt{s_{{}_{NN}}}$ = 200 GeV
• Polarization and Vorticity in the Quark Gluon Plasma
• Relativistic hydrodynamics for spin-polarized fluids
• Relativistic Viscous Fluid Dynamics and Non-Equilibrium Entropy
• Shear-induced spin polarization in heavy-ion collisions
• Fate of spin polarization in a relativistic fluid: An entropy-current analysis
• Polarization of massive fermions in a vortical fluid
• Generating spin polarization from vorticity through nonlocal collisions
• Global $\Lambda$ Polarization in high energy collisions
• Lambda hyperon polarization in relativistic heavy ion collisions from the chiral kinetic approach
• Relativistic dissipative spin dynamics in the relaxation time approximation
• Relativistic Quantum Kinetic Theory for Massive Fermions and Spin Effects
• Spin tensor and its role in non-equilibrium thermodynamics
• Spin Hydrodynamics and Symmetric Energy-Momentum Tensors -- A current induced by the spin vorticity --
• Kubo formulas for relativistic fluids in strong magnetic fields
• Hydrodynamics of spin currents
• Axial Kinetic Theory and Spin Transport for Fermions with Arbitrary Mass
• From Chiral Kinetic Theory To Relativistic Viscous Spin Hydrodynamics
• Non-dissipative second-order transport, spin, and pseudo-gauge transformations in hydrodynamics
• The ideal relativistic fluid limit for a medium with polarization
• The ideal relativistic spinning gas: polarization and spectra
• The ideal relativistic rotating gas as a perfect fluid with spin
• Effective quantum kinetic theory for spin transport of fermions with collsional effects
• Covariant Spin Kinetic Theory I: Collisionless Limit
• Linear response theory of relativistic hydrodynamics with spin
• Longitudinal spin polarization in a thermal model
• Causality and dissipation in relativistic polarizeable fluids
• Quantum Kinetic Theory of Spin Polarization of Massive Quarks in Perturbative QCD: Leading Log
• Relativistic Viscous Hydrodynamics with Angular Momentum
• Sound waves and vortices in a polarized relativistic fluid
• Analytic solutions of relativistic dissipative spin hydrodynamics with Bjorken expansion
• Relativistic second-order spin hydrodynamics: an entropy-current analysis
• Light-Meson Spectroscopy with COMPASS
• Complete relativistic second-order dissipative hydrodynamics from the entropy principle
• Nonequilibrium Thermodynamical Inequivalence of Quantum Stress-energy and Spin Tensors
• Hydrodynamics, spin currents and torsion
• Polarization phenomenon in heavy-ion collisions
• Kubo formulae for first-order spin hydrodynamics
• Extensivity, entropy current, area law and Unruh effect
• Boost invariant spin hydrodynamics within the first order in derivative expansion
• Generalized thermodynamic relations for perfect spin hydrodynamics
• Cross effects in spin hydrodynamics: A revisit Entropy analysis and statistical operator
• Boost-invariant spin hydrodynamics with spin feedback effects
• Relativistic second-order spin hydrodynamics: A Kubo-type formulation for the quark-gluon plasma
• Polarization of spin-1/2 particles with effective spacetime dependent masses

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