A dissipative spin hydrodynamic framework and Kubo formula: Spin chemical potential as the leading order term in the hydrodynamic gradient expansion

Abstract

Using the entropy current analysis, we develop a Naiver-Stokes theory of dissipative spin hydrodynamic framework. Here, we consider that the spin chemical potential () is a leading order term () in the hydrodynamic gradient expansion. For consistency of the framework, the energy–momentum tensor needs to be symmetric up to first order in the gradient expansion. The spin tensor is antisymmetric only in the last two indices. Moreover, by applying Zubarev’s non-equilibrium statistical operator method, we find the Kubo relations for various transport coefficients, including spin transport coefficients appearing in the spin hydrodynamic description.