  Spin evolution opened a large field in quantum plasma research. The spin
waves in plasmas were considered among new phenomena considered in spin-1/2
quantum plasmas. The spin density evolution equation found by means of the
many-particle quantum hydrodynamics shows existence of the "thermal" part of
the spin current, which is an analog of the thermal pressure, or the Fermi
pressure for degenerate electron gas, existing in the Euler equation. However,
this term has been dropped, since there has not been found any equation of
state for the thermal part of the spin current (TPSC), like we have for the
pressure. In this paper we derive the equation of state for the TPSC and apply
it for study of spectrum of collective excitations in spin-1/2 quantum plasmas.
We focus our research on the spectrum of spin waves, since this spectrum is
affected by the thermal part of the spin current. We consider two kinds of
plasmas: electron-ion plasma with motionless ions and degenerate electrons, and
degenerate electron-positron plasmas. We also present the non-linear Pauli
equation with the spinor pressure term containing described effects. The
thermal part of the flux of spin current existing in the spin current evolution
equation is also derived. We also consider the contribution of the TPSC in the
grand generalized vorticity evolution.
