Extending Israel and Stewart hydrodynamics to relativistic superfluids via Carter's multifluid approach

Abstract

We construct a relativistic model for bulk viscosity and heat conduction in a superfluid. Building on the principles of Unified Extended Irreversible Thermodynamics, the model is derived from Carter's multifluid approach for a theory with 3 four-currents: particles, entropy, and quasi-particles. Dissipation arises directly from the fact that the quasi-particle four-current is an independent degree of freedom that does not necessarily comove with the entropy. For small deviations from local thermodynamic equilibrium, the model provides an extension of the Israel-Stewart theory to superfluid systems. It can, therefore, be made hyperbolic, causal and stable if the microscopic input is accurate. The non-dissipative limit of the model is the relativistic two-fluid model of Carter, Khalatnikov and Gusakov. The Newtonian limit of the model is an Extended-Irreversible-Thermodynamic extension of Landau's two-fluid model. The model predicts the existence of four bulk viscosity coefficients and accounts for their microscopic origin, providing their exact formulas in terms of the quasi-particle creation rate. Furthermore, when fast oscillations of small amplitude around the equilibrium are considered, the relaxation-time term in the telegraph-type equations for the bulk viscosities accounts directly for their expected dependence on the frequency.

34 pages, 1 figure

References in corpus (13)

• Superfluidity and Superconductivity in Neutron Stars
• Superfluid Heat Conduction and the Cooling of Magnetized Neutron Stars
• Bulk viscosity of superfluid neutron stars
• Thermal Dynamics in General Relativity
• When the entropy has no maximum: A new perspective on the instability of the first-order theories of dissipation
• Temperature-dependent pulsations of superfluid neutron stars
• Global numerical simulations of the rise of vortex-mediated pulsar glitches in full general relativity
• Applying the Gibbs stability criterion to relativistic hydrodynamics
• Unified Extended Irreversible Thermodynamics and the stability of relativistic theories for dissipation
• Transport theory for cold relativistic superfluids from an analogue model of gravity
• Relativistic Kinetics of Phonon Gas in Superfluids
• Superfluid dynamics in neutron star crusts: the Iordanskii force and chemical gauge covariance
• Proving the Lorentz invariance of the entropy and the covariance of thermodynamics