Dissipative currents and transport coefficients in relativistic spin hydrodynamics

TL;DR

The authors derive the most general first-order dissipative currents in relativistic spin hydrodynamics with finite chemical potential by decomposing gradients of thermo-hydrodynamic fields into an SO(3) irreducible basis and enforcing matching conditions plus entropy-positivity. This yields 23 independent transport coefficients that relate gradients to dissipative currents in the symmetric and antisymmetric parts of the energy-momentum tensor, the conserved current, and the spin tensor, including new spin-gradient channels. The results connect to quantum kinetic theory through precise identifications of hydrodynamic coefficients with kinetic-theory parameters, and they identify a consistent Navier–Stokes limit for spin hydrodynamics while highlighting new transport channels arising from spin-potential gradients. The work provides a concrete, testable framework for spin hydrodynamics applicable to the quark-gluon plasma and related systems, with clear avenues for numerical implementation and further microscopic validation.

Abstract

We determine the form of dissipative currents at the first order in relativistic spin hydrodynamics with finite chemical potential including gradients of the spin potential. Taking advantage of isotropy in the hydrodynamic local rest frame, using a suitable matching condition for the flow velocity and enforcing the semi-positivity of entropy production, we find 23 dissipative transport coefficients relating dissipative currents to gradients of the thermo-hydrodynamic fields: 4 for the symmetric part of the energy-momentum tensor, 5 for the antisymmetric part, 3 for the conserved vector current, and 11 for the spin tensor. We compare our finding with previous results in literature.

Figures (2)

• Figure 1: Three-dimensional foliation of initial Cauchy space-like hyperspace $\Sigma_{(0)}$, with volume $\Omega$, and present time hypersurface $\Sigma_{(t)}$, where $\hat{n}$ is chosen to be the fluid four-velocity.
• Figure 2: Left: The transport coefficients that have to be semipositive also in hydrodynamics without spin. Right: The additional coefficients that have to be semipositive in spin hydrodynamics. Here, $G$ denotes the coupling strengh of the four-fermi interaction. Note that we multiplied the coefficients $\Gamma^{(\kappa)}$ and $\Gamma^{(\omega)}$ by $z^2$ to render the result finite.