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

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 quasiparticles. Dissipation arises directly from the fact that the quasiparticle 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 nondissipative 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 quasiparticle 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.