A theory for non-Abelian superfluid dynamics

We write down a theory for non-Abelian superfluids with a partially broken (semisimple) Lie group. We adapt the offshell formalism of hydrodynamics to superfluids and use it to comment on the superfluid transport compatible with the second law of thermodynamics. We find that the second law can be also used to derive the Josephson equation, which governs dynamics of the Goldstone modes. In the course of our analysis, we derive an alternate and mutually distinct parametrization of the recently proposed classification of hydrodynamic transport and generalize it to superfluids.