  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.
