Nondissipative Second-Order Transport, Spin, and Pseudogauge Transformations in Hydrodynamics

We derive a set of nontrivial relations between second-order transport coefficients which follow from the second law of thermodynamics upon considering a regime close to uniform rotation of the fluid. We demonstrate that an extension of hydrodynamics by spin variable is equivalent to modifying conventional hydrodynamics by a set of second-order terms satisfying the relations we derived. We point out that a novel contribution to the heat current orthogonal to vorticity and temperature gradient reminiscent of the thermal Hall effect is constrained by the second law.