Non-dissipative second-order transport, spin, and pseudo-gauge transformations in hydrodynamics

TL;DR

This paper derives relations between second-order transport coefficients in hydrodynamics considering spin and pseudo-gauge transformations, revealing new constraints and extensions to conventional hydrodynamics near uniform rotation.

Contribution

It introduces a novel framework linking spin variables and second-order hydrodynamics, establishing new thermodynamic constraints and extending the theory.

Findings

Relations between second-order transport coefficients derived from the second law

Extension of hydrodynamics by spin variables equivalent to second-order modifications

Identification of a thermal Hall-like heat current constrained by thermodynamics

Abstract

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 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.