  The hydrodynamic model including the spin degree of freedom and the
electromagnetic field was discussed. In this derivation, we applied
electromagnetism for macroscopic medium proposed by Minkowski. For the equation
of motion of spin, we assumed that the hydrodynamic representation of the Pauli
equation is reproduced when the many-body effect is neglected. Then the
spin-magnetic interaction in the Pauli equation was converted to a part of the
magnetization. The fluid and spin stress tensors induced by the many-body
effect were obtained by employing the algebraic positivity of the entropy
production in the framework of the linear irreversible thermodynamics,
including the mixing effect of the irreversible currents. We further
constructed the constitutive equation of the polarization and the
magnetization. Our polarization equation is more reasonable compared to another
result obtained using electromagnetism for macroscopic medium proposed by de
Groot-Mazur.
