  General nonequilibrium quantum transport equations are derived for a coupled
system of charge carriers, Dirac spin, isospin (or valley spin), and
pseudospin, such as either one of the band, layer, impurity, and boundary
pseudospins. Limiting cases are obtained for one, two or three different kinds
of spin ocurring in a system. We show that a characteristic integer number
$N_{s}$ determines the formal form of spin quantum transport equations,
irrespective of the type of spins or pseudospins, as well as the maximal
entanglement entropy. The results may shed a new perspective on the mechanism
leading to zero modes and chiral/helical edge states in topological insulators,
integer quantum Hall effect topological insulator (QHE-TI), quantum spin Hall
effect topological insulator (QSHE-TI) and Kondo topological insulator
(Kondo-TI). It also shed new light in the observed competing weak localization
and antilocalization in spin-dependent quantum transport measurements. In
particular, a novel mechanism of localization and delocalization, as well as
the new mechanism leading to the onset of superconductivity in bilayer systems
seems to emerge naturally from torque entanglements in nonequilibrium quantum
transport equations of spin and pseudospins. Moreover, the general results may
serve as a foundation for engineering approximations of the quantum transport
simulations of spintronic devices based on graphene and other 2-D materials
such as the transition metal dichalcogenides (TMDs), as well as based on
topological materials exhibiting quantum spin Hall effects. The extension of
the formalism to spincaloritronics and pseudo-spincaloritronics is
straightforward.
